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Code Libraries

[Nd] PHP Classes

These libraries where written and used as part of the [Nd] framework codebase.
Useful PHP Classes

These libraries are covered under their respective Licenses.
Code Repository

The code libraries listed to the right -> are available for public use. You may copy, distribute, and eat this code as you wish. However, the license remains in effect for the life of the software.
Pretense for download and use "[Nd] Libraries":
You may not use this code in a commercial setting without prior consent from [Nd].
You may not misrepresent yourself as the author of this code.
You may make changes to this code, but must make the changes available under this license.
These libraries are governed by their respective licenses.
<?php
    
$BUFFEROUTPUT = true;    
    
/**
  * Prime number check
  *
  * php 5
  *
  * 
  * LICENSE: Use of this library is governed by the Creative Commons License Attribution 2.5. 
  * You can check it out at: http://creativecommons.org/licenses/by/2.5/legalcode
  *
  * - You may copy, distribute, and eat this code as you wish. You must give me credit for
  * writing it. You may not misrepresent yourself as the author of this code.
  * - You may not use this code in a commercial setting without prior consent from me.
  * - If you make changes to this code, you must make the changes available under a license like
  * this one.
  *
  * @category   Prime number check 
  * @author     R. Fritz Washabaugh <general@nucleusdevelopment.com>
  * @copyright  2011 Nucleus Development - R. Fritz Washabaugh
  * @license    http://creativecommons.org/licenses/by/2.5/legalcode CC 2.5
  * @link       http://www.nucleusdevelopment.com.com/code/do/prime
  *
  **/
/**
  * DEMO HERE:
  *    
  * http://nkdv.co/3B
  */    
    
 
// get the prime from the form or get var
if(isset($_REQUEST['num'])){
    $num = get_magic_quotes_gpc() 
        ? stripslashes( trim( $_REQUEST['num'] ) ) 
        : trim( $_REQUEST['num'] );
    $num = str_replace("Enter a number ", '', $num);
}
 
 
// if number is set check it for prime
if( isset( $num ) ) {    
 
    $num = preg_replace( '/[\nA-Za-z,.]+/','', $num);
    $num = explode( ' ', $num );
        
    // return false if no number
    if( !is_numeric( $num[0] ) )
        die( 'Enter a number ' );
    
    // no incrumentation just find prime
    if( !isset( $num[1] ) )
        if( true !== ($r = isPrime( $num[0] ) ) ) 
            die ($r);
        else
            die ('prime');
 
    // we are incrumenting 
    // if we try to search for a prime that 
    // is too big error out.
    if( (int)$num[1] > 10 )    
        die('error: needle to large');
    
    $count = 0;
    
    // loop through number set checking for prime of $num[1] length
    while( 
        true !== ( $r = isPrime( substr( $num[0], $count, $num[1] ) ) ) 
        && 
        ( $count++ + $num[1] < strlen( (string)$num[0] ) ) 
    );
    
    // Loop either reached end or short circuited because it found prime
    if( $r !== true ) {
        die('no prime numbers found');
    } else {
        die( 'prime found, ['. substr( $num[0], $count, $num[1] ).'] at digit ' . $count );
    }
}    
 
 
function isPrime($num) {    
    
    // use $sr for square root of num
    $sr = $num;
            
    // one is special and not prime 
    if($num == 1)
        return 'not prime';
    
    // easy small numbers are prime, no fancy math needed
    if($num == 2 || $num == 3 || $num == 5 || $num == 7)
        return true;
        
    // find square root for later use
    if( $sr > 8 ) {
        $sr = sqrt( $sr );
        
        // the sq rt is an integer it's not prime
        if(  $sr == round( $sr ) )
            return 'not prime, square root is ' . $sr;
    }    
 
    // divisible by 2
    if( $num / 2 == round( $num / 2 ) )
        return 'not prime, divisible by 2';
 
    // divisible by 5
    if( $num / 5 == round( $num / 5 ) )
        return 'not prime, divisible by 5';
 
    // alt method for finding composite numbers
    $comp = 0;
    for($i = 0; $i < strlen( (string)$num ); $i++ )
        $comp += $num[$i];
        
    if($comp % 3 == 0)
        return 'not prime, composite divisible by 3';
        
    /**
      * Now the fun part
      * start dividing by every prime
      * up to the square root of the number in question.
      */
      $primes = array( 
        11, 13, 17, 19, 23, 29, 31, 37,  
         41, 43, 47, 53, 59, 61, 67, 71,  
         73, 79, 83, 89, 97, 101, 103, 107,  
         109, 113, 127, 131, 137, 139, 149, 151,  
         157, 163, 167, 173, 179, 181, 191, 193,  
         197, 199, 211, 223, 227, 229, 233, 239,  
         241, 251, 257, 263, 269, 271, 277, 281,  
         283, 293, 307, 311, 313, 317, 331, 337,  
         347, 349, 353, 359, 367, 373, 379, 383,  
         389, 397, 401, 409, 419, 421, 431, 433,  
         439, 443, 449, 457, 461, 463, 467, 479,  
         487, 491, 499, 503, 509, 521, 523, 541,  
         547, 557, 563, 569, 571, 577, 587, 593,  
         599, 601, 607, 613, 617, 619, 631, 641,  
         643, 647, 653, 659, 661, 673, 677, 683,  
         691, 701, 709, 719, 727, 733, 739, 743,  
         751, 757, 761, 769, 773, 787, 797, 809,  
         811, 821, 823, 827, 829, 839, 853, 857,  
         859, 863, 877, 881, 883, 887, 907, 911,  
         919, 929, 937, 941, 947, 953, 967, 971,  
         977, 983, 991, 997, 1009, 1013, 1019, 1021,  
         1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,  
         1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123,  
         1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193,  
         1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,  
         1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301,  
         1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,  
         1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439,  
         1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487,  
         1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549,  
         1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,  
         1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,  
         1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721,  
         1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783,  
         1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861,  
         1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,  
         1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,  
         1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029,  
         2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,  
         2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143,  
         2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237,  
         2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,  
         2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347,  
         2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393,  
         2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459,  
         2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543,  
         2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,  
         2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677,  
         2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713,  
         2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777,  
         2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837,  
         2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,  
         2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969,  
         2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041,  
         3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119,  
         3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191,  
         3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,  
         3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,  
         3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373,  
         3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461,  
         3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527,  
         3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571,  
         3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631,  
         3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697,  
         3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767,  
         3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833,  
         3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,  
         3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947,  
         3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,  
         4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093,  
         4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157,  
         4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,  
         4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283,  
         4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363,  
         4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447,  
         4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513,  
         4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,  
         4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649,  
         4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721,  
         4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,  
         4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871,  
         4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,  
         4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993,  
         4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051,  
         5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113,  
         5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197,  
         5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,  
         5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,  
         5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419,  
         5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479,  
         5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,  
         5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,  
         5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683,  
         5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743,  
         5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821,  
         5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867,  
         5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,  
         5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043,  
         6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101,  
         6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173,  
         6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247,  
         6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,  
         6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359,  
         6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427,  
         6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529,  
         6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581,  
         6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,  
         6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733,  
         6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803,  
         6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869,  
         6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949,  
         6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,  
         7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069,  
         7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159,  
         7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229,  
         7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309,  
         7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,  
         7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487,  
         7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541,  
         7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589,  
         7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669,  
         7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,  
         7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817,  
         7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,  
         7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949,  
         7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053,  
         8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111,  
         8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191,  
         8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263,  
         8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317,  
         8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419,  
         8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501,  
         8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573,  
         8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641,  
         8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699,  
         8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753,  
         8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831,  
         8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893,  
         8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971,  
         8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043,  
         9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133,  
         9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199,  
         9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277,  
         9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341,  
         9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413,  
         9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463,  
         9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533,  
         9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623,  
         9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689,  
         9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767,  
         9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829,  
         9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887,  
         9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967,  
         9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069,  
         10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139,  
         10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193,  
         10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271,  
         10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333,  
         10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429,  
         10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499,  
         10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597,  
         10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657,  
         10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729,  
         10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831,  
         10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889,  
         10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973,  
         10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059,  
         11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119,  
         11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197,  
         11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279,  
         11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353,  
         11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443,  
         11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503,  
         11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597,  
         11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699,  
         11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783,  
         11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833,  
         11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923,  
         11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971,  
         11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049,  
         12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119,  
         12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211,  
         12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277,  
         12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373,  
         12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433,  
         12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497,  
         12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553,  
         12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619,  
         12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697,  
         12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781,  
         12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853,  
         12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923,  
         12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001,  
         13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063,  
         13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151,  
         13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219,  
         13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309,  
         13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397,  
         13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463,  
         13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553,  
         13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633,  
         13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697,  
         13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759,  
         13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841,  
         13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907,  
         13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999,  
         14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081,  
         14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173,  
         14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281,  
         14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369,  
         14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431,  
         14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519,  
         14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563,  
         14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653,  
         14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731,  
         14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779,  
         14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851,  
         14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929,  
         14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017,  
         15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101,  
         15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173,  
         15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259,  
         15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307,  
         15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373,  
         15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443,  
         15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527,  
         15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607,  
         15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667,  
         15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739,  
         15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803,  
         15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889,  
         15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971,  
         15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063,  
         16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111,  
         16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217,  
         16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301,  
         16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381,  
         16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453,  
         16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553,  
         16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633,  
         16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699,  
         16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811,  
         16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889,  
         16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963,  
         16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029,  
         17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107,  
         17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191,  
         17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293,  
         17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359,  
         17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419,  
         17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489,  
         17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573,  
         17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657,  
         17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737,  
         17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827,  
         17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909,  
         17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971,  
         17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047,  
         18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121,  
         18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191,  
         18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253,  
         18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313,  
         18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401,  
         18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461,  
         18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541,  
         18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671,  
         18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749,  
         18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859,  
         18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959,  
         18973, 18979, 19001, 19009, 19013, 19031, 19037, 19051,  
         19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141,  
         19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219,  
         19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301,  
         19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391,  
         19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441,  
         19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489,  
         19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571,  
         19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687,  
         19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753,  
         19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841,  
         19843, 19853, 19861, 19867, 19889, 19891, 19913, 19919,  
         19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991,  
         19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051,  
         20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123,  
         20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183,  
         20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287,  
         20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357,  
         20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431,  
         20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521,  
         20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611,  
         20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717,  
         20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771,  
         20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879,  
         20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947,  
         20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017,  
         21019, 21023, 21031, 21059, 21061, 21067, 21089, 21101,  
         21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169,  
         21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247,  
         21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341,  
         21347, 21377, 21379, 21383, 21391, 21397, 21401, 21407,  
         21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499,  
         21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563,  
         21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613,  
         21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713,  
         21727, 21737, 21739, 21751, 21757, 21767, 21773, 21787,  
         21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859,  
         21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943,  
         21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031,  
         22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091,  
         22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153,  
         22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259,  
         22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307,  
         22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409,  
         22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501,  
         22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573,  
         22613, 22619, 22621, 22637, 22639, 22643, 22651, 22669,  
         22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727,  
         22739, 22741, 22751, 22769, 22777, 22783, 22787, 22807,  
         22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901,  
         22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993,  
         23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041,  
         23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099,  
         23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197,  
         23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291,  
         23293, 23297, 23311, 23321, 23327, 23333, 23339, 23357,  
         23369, 23371, 23399, 23417, 23431, 23447, 23459, 23473,  
         23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561,  
         23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623,  
         23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687,  
         23689, 23719, 23741, 23743, 23747, 23753, 23761, 23767,  
         23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833,  
         23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909,  
         23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993,  
         24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061,  
         24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109,  
         24113, 24121, 24133, 24137, 24151, 24169, 24179, 24181,  
         24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281,  
         24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391,  
         24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473,  
         24481, 24499, 24509, 24517, 24527, 24533, 24547, 24551,  
         24571, 24593, 24611, 24623, 24631, 24659, 24671, 24677,  
         24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767,  
         24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851,  
         24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943,  
         24953, 24967, 24971, 24977, 24979, 24989, 25013, 25031,  
         25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117,  
         25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183,  
         25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261,  
         25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349,  
         25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439,  
         25447, 25453, 25457, 25463, 25469, 25471, 25523, 25537,  
         25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603,  
         25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673,  
         25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759,  
         25763, 25771, 25793, 25799, 25801, 25819, 25841, 25847,  
         25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931,  
         25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999,  
         26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099,  
         26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171,  
         26177, 26183, 26189, 26203, 26209, 26227, 26237, 26249,  
         26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317,  
         26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399,  
         26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479,  
         26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573,  
         26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681,  
         26683, 26687, 26693, 26699, 26701, 26711, 26713, 26717,  
         26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801,  
         26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879,  
         26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951,  
         26953, 26959, 26981, 26987, 26993, 27011, 27017, 27031,  
         27043, 27059, 27061, 27067, 27073, 27077, 27091, 27103,  
         27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211,  
         27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283,  
         27299, 27329, 27337, 27361, 27367, 27397, 27407, 27409,  
         27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487,  
         27509, 27527, 27529, 27539, 27541, 27551, 27581, 27583,  
         27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691,  
         27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751,  
         27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803,  
         27809, 27817, 27823, 27827, 27847, 27851, 27883, 27893,  
         27901, 27917, 27919, 27941, 27943, 27947, 27953, 27961,  
         27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051,  
         28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111,  
         28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219,  
         28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309,  
         28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411,  
         28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499,  
         28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571,  
         28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621,  
         28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669,  
         28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753,  
         28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837,  
         28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921,  
         28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021,  
         29023, 29027, 29033, 29059, 29063, 29077, 29101, 29123,  
         29129, 29131, 29137, 29147, 29153, 29167, 29173, 29179,  
         29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251,  
         29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339,  
         29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411,  
         29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501,  
         29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587,  
         29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671,  
         29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789,  
         29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873,  
         29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983,  
         29989, 30011, 30013, 30029, 30047, 30059, 30071, 30089,  
         30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137,  
         30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211,  
         30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307,  
         30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391,  
         30403, 30427, 30431, 30449, 30467, 30469, 30491, 30493,  
         30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559,  
         30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671,  
         30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757,  
         30763, 30773, 30781, 30803, 30809, 30817, 30829, 30839,  
         30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893,  
         30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983,  
         31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079,  
         31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153,  
         31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223,  
         31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271,  
         31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357,  
         31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481,  
         31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547,  
         31567, 31573, 31583, 31601, 31607, 31627, 31643, 31649,  
         31657, 31663, 31667, 31687, 31699, 31721, 31723, 31727,  
         31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817,  
         31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957,  
         31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029,  
         32051, 32057, 32059, 32063, 32069, 32077, 32083, 32089,  
         32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183,  
         32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257,  
         32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327,  
         32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381,  
         32401, 32411, 32413, 32423, 32429, 32441, 32443, 32467,  
         32479, 32491, 32497, 32503, 32507, 32531, 32533, 32537,  
         32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609,  
         32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707,  
         32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789,  
         32797, 32801, 32803, 32831, 32833, 32839, 32843, 32869,  
         32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957,  
         32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023,  
         33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091,  
         33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181,  
         33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289,  
         33301, 33311, 33317, 33329, 33331, 33343, 33347, 33349,  
         33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427,  
         33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521,  
         33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587,  
         33589, 33599, 33601, 33613, 33617, 33619, 33623, 33629,  
         33637, 33641, 33647, 33679, 33703, 33713, 33721, 33739,  
         33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797,  
         33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871,  
         33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961,  
         33967, 33997, 34019, 34031, 34033, 34039, 34057, 34061,  
         34123, 34127, 34129, 34141, 34147, 34157, 34159, 34171,  
         34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261,  
         34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319,  
         34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403,  
         34421, 34429, 34439, 34457, 34469, 34471, 34483, 34487,  
         34499, 34501, 34511, 34513, 34519, 34537, 34543, 34549,  
         34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649,  
         34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721,  
         34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807,  
         34819, 34841, 34843, 34847, 34849, 34871, 34877, 34883,  
         34897, 34913, 34919, 34939, 34949, 34961, 34963, 34981,  
         35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083,  
         35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149,  
         35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257,  
         35267, 35279, 35281, 35291, 35311, 35317, 35323, 35327,  
         35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419,  
         35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509,  
         35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573,  
         35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729,  
         35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803,  
         35809, 35831, 35837, 35839, 35851, 35863, 35869, 35879,  
         35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969,  
         35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017,  
         36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109,  
         36131, 36137, 36151, 36161, 36187, 36191, 36209, 36217,  
         36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299,  
         36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383,  
         36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479,  
         36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559,  
         36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637,  
         36643, 36653, 36671, 36677, 36683, 36691, 36697, 36709,  
         36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781,  
         36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857,  
         36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923,  
         36929, 36931, 36943, 36947, 36973, 36979, 36997, 37003,  
         37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087,  
         37097, 37117, 37123, 37139, 37159, 37171, 37181, 37189,  
         37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277,  
         37307, 37309, 37313, 37321, 37337, 37339, 37357, 37361,  
         37363, 37369, 37379, 37397, 37409, 37423, 37441, 37447,  
         37463, 37483, 37489, 37493, 37501, 37507, 37511, 37517,  
         37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573,  
         37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649,  
         37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781,  
         37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861,  
         37871, 37879, 37889, 37897, 37907, 37951, 37957, 37963,  
         37967, 37987, 37991, 37993, 37997, 38011, 38039, 38047,  
         38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167,  
         38177, 38183, 38189, 38197, 38201, 38219, 38231, 38237,  
         38239, 38261, 38273, 38281, 38287, 38299, 38303, 38317,  
         38321, 38327, 38329, 38333, 38351, 38371, 38377, 38393,  
         38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543,  
         38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611,  
         38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693,  
         38699, 38707, 38711, 38713, 38723, 38729, 38737, 38747,  
         38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839,  
         38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921,  
         38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019,  
         39023, 39041, 39043, 39047, 39079, 39089, 39097, 39103,  
         39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163,  
         39181, 39191, 39199, 39209, 39217, 39227, 39229, 39233,  
         39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323,  
         39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397,  
         39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503,  
         39509, 39511, 39521, 39541, 39551, 39563, 39569, 39581,  
         39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679,  
         39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769,  
         39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841,  
         39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901,  
         39929, 39937, 39953, 39971, 39979, 39983, 39989, 40009,  
         40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099,  
         40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169,  
         40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253,  
         40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387,  
         40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487,  
         40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559,  
         40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639,  
         40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763,  
         40771, 40787, 40801, 40813, 40819, 40823, 40829, 40841,  
         40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903,  
         40927, 40933, 40939, 40949, 40961, 40973, 40993, 41011,  
         41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081,  
         41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177,  
         41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227,  
         41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299,  
         41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399,  
         41411, 41413, 41443, 41453, 41467, 41479, 41491, 41507,  
         41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593,  
         41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641,  
         41647, 41651, 41659, 41669, 41681, 41687, 41719, 41729,  
         41737, 41759, 41761, 41771, 41777, 41801, 41809, 41813,  
         41843, 41849, 41851, 41863, 41879, 41887, 41893, 41897,  
         41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959,  
         41969, 41981, 41983, 41999, 42013, 42017, 42019, 42023,  
         42043, 42061, 42071, 42073, 42083, 42089, 42101, 42131,  
         42139, 42157, 42169, 42179, 42181, 42187, 42193, 42197,  
         42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283,  
         42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359,  
         42373, 42379, 42391, 42397, 42403, 42407, 42409, 42433,  
         42437, 42443, 42451, 42457, 42461, 42463, 42467, 42473,  
         42487, 42491, 42499, 42509, 42533, 42557, 42569, 42571,  
         42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677,  
         42683, 42689, 42697, 42701, 42703, 42709, 42719, 42727,  
         42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797,  
         42821, 42829, 42839, 42841, 42853, 42859, 42863, 42899,  
         42901, 42923, 42929, 42937, 42943, 42953, 42961, 42967,  
         42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051,  
         43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159,  
         43177, 43189, 43201, 43207, 43223, 43237, 43261, 43271,  
         43283, 43291, 43313, 43319, 43321, 43331, 43391, 43397,  
         43399, 43403, 43411, 43427, 43441, 43451, 43457, 43481,  
         43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579,  
         43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649,  
         43651, 43661, 43669, 43691, 43711, 43717, 43721, 43753,  
         43759, 43777, 43781, 43783, 43787, 43789, 43793, 43801,  
         43853, 43867, 43889, 43891, 43913, 43933, 43943, 43951,  
         43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017,  
         44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087,  
         44089, 44101, 44111, 44119, 44123, 44129, 44131, 44159,  
         44171, 44179, 44189, 44201, 44203, 44207, 44221, 44249,  
         44257, 44263, 44267, 44269, 44273, 44279, 44281, 44293,  
         44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449,  
         44453, 44483, 44491, 44497, 44501, 44507, 44519, 44531,  
         44533, 44537, 44543, 44549, 44563, 44579, 44587, 44617,  
         44621, 44623, 44633, 44641, 44647, 44651, 44657, 44683,  
         44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771,  
         44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843,  
         44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927,  
         44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007,  
         45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127,  
         45131, 45137, 45139, 45161, 45179, 45181, 45191, 45197,  
         45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307,  
         45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377,  
         45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491,  
         45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569,  
         45587, 45589, 45599, 45613, 45631, 45641, 45659, 45667,  
         45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757,  
         45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833,  
         45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949,  
         45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049,  
         46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133,  
         46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199,  
         46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301,  
         46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399,  
         46411, 46439, 46441, 46447, 46451, 46457, 46471, 46477,  
         46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567,  
         46573, 46589, 46591, 46601, 46619, 46633, 46639, 46643,  
         46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723,  
         46727, 46747, 46751, 46757, 46769, 46771, 46807, 46811,  
         46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877,  
         46889, 46901, 46919, 46933, 46957, 46993, 46997, 47017,  
         47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119,  
         47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189,  
         47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293,  
         47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363,  
         47381, 47387, 47389, 47407, 47417, 47419, 47431, 47441,  
         47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527,  
         47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609,  
         47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699,  
         47701, 47711, 47713, 47717, 47737, 47741, 47743, 47777,  
         47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843,  
         47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939,  
         47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023,  
         48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121,  
         48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221,  
         48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313,  
         48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409,  
         48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487,  
         48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563,  
         48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649,  
         48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757,  
         48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817,  
         48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883,  
         48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003,  
         49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069,  
         49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157,  
         49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211,  
         49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331,  
         49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409,  
         49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477,  
         49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549,  
         49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663,  
         49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741,  
         49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811,  
         49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919,  
         49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993,  
         49999, 50021, 50023, 50033, 50047, 50051, 50053, 50069,  
         50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129,  
         50131, 50147, 50153, 50159, 50177, 50207, 50221, 50227,  
         50231, 50261, 50263, 50273, 50287, 50291, 50311, 50321,  
         50329, 50333, 50341, 50359, 50363, 50377, 50383, 50387,  
         50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503,  
         50513, 50527, 50539, 50543, 50549, 50551, 50581, 50587,  
         50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683,  
         50707, 50723, 50741, 50753, 50767, 50773, 50777, 50789,  
         50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891,  
         50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971,  
         50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061,  
         51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169,  
         51193, 51197, 51199, 51203, 51217, 51229, 51239, 51241,  
         51257, 51263, 51283, 51287, 51307, 51329, 51341, 51343,  
         51347, 51349, 51361, 51383, 51407, 51413, 51419, 51421,  
         51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479,  
         51481, 51487, 51503, 51511, 51517, 51521, 51539, 51551,  
         51563, 51577, 51581, 51593, 51599, 51607, 51613, 51631,  
         51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713,  
         51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803,  
         51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871,  
         51893, 51899, 51907, 51913, 51929, 51941, 51949, 51971,  
         51973, 51977, 51991, 52009, 52021, 52027, 52051, 52057,  
         52067, 52069, 52081, 52103, 52121, 52127, 52147, 52153,  
         52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237,  
         52249, 52253, 52259, 52267, 52289, 52291, 52301, 52313,  
         52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433,  
         52453, 52457, 52489, 52501, 52511, 52517, 52529, 52541,  
         52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609,  
         52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709,  
         52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783,  
         52807, 52813, 52817, 52837, 52859, 52861, 52879, 52883,  
         52889, 52901, 52903, 52919, 52937, 52951, 52957, 52963,  
         52967, 52973, 52981, 52999, 53003, 53017, 53047, 53051,  
         53069, 53077, 53087, 53089, 53093, 53101, 53113, 53117,  
         53129, 53147, 53149, 53161, 53171, 53173, 53189, 53197,  
         53201, 53231, 53233, 53239, 53267, 53269, 53279, 53281,  
         53299, 53309, 53323, 53327, 53353, 53359, 53377, 53381,  
         53401, 53407, 53411, 53419, 53437, 53441, 53453, 53479,  
         53503, 53507, 53527, 53549, 53551, 53569, 53591, 53593,  
         53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639,  
         53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731,  
         53759, 53773, 53777, 53783, 53791, 53813, 53819, 53831,  
         53849, 53857, 53861, 53881, 53887, 53891, 53897, 53899,  
         53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993,  
         54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091,  
         54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181,  
         54193, 54217, 54251, 54269, 54277, 54287, 54293, 54311,  
         54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377,  
         54401, 54403, 54409, 54413, 54419, 54421, 54437, 54443,  
         54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521,  
         54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583,  
         54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673,  
         54679, 54709, 54713, 54721, 54727, 54751, 54767, 54773,  
         54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877,  
         54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973,  
         54979, 54983, 55001, 55009, 55021, 55049, 55051, 55057,  
         55061, 55073, 55079, 55103, 55109, 55117, 55127, 55147,  
         55163, 55171, 55201, 55207, 55213, 55217, 55219, 55229,  
         55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337,  
         55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439,  
         55441, 55457, 55469, 55487, 55501, 55511, 55529, 55541,  
         55547, 55579, 55589, 55603, 55609, 55619, 55621, 55631,  
         55633, 55639, 55661, 55663, 55667, 55673, 55681, 55691,  
         55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793,  
         55799, 55807, 55813, 55817, 55819, 55823, 55829, 55837,  
         55843, 55849, 55871, 55889, 55897, 55901, 55903, 55921,  
         55927, 55931, 55933, 55949, 55967, 55987, 55997, 56003,  
         56009, 56039, 56041, 56053, 56081, 56087, 56093, 56099,  
         56101, 56113, 56123, 56131, 56149, 56167, 56171, 56179,  
         56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267,  
         56269, 56299, 56311, 56333, 56359, 56369, 56377, 56383,  
         56393, 56401, 56417, 56431, 56437, 56443, 56453, 56467,  
         56473, 56477, 56479, 56489, 56501, 56503, 56509, 56519,  
         56527, 56531, 56533, 56543, 56569, 56591, 56597, 56599,  
         56611, 56629, 56633, 56659, 56663, 56671, 56681, 56687,  
         56701, 56711, 56713, 56731, 56737, 56747, 56767, 56773,  
         56779, 56783, 56807, 56809, 56813, 56821, 56827, 56843,  
         56857, 56873, 56891, 56893, 56897, 56909, 56911, 56921,  
         56923, 56929, 56941, 56951, 56957, 56963, 56983, 56989,  
         56993, 56999, 57037, 57041, 57047, 57059, 57073, 57077,  
         57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149,  
         57163, 57173, 57179, 57191, 57193, 57203, 57221, 57223,  
         57241, 57251, 57259, 57269, 57271, 57283, 57287, 57301,  
         57329, 57331, 57347, 57349, 57367, 57373, 57383, 57389,  
         57397, 57413, 57427, 57457, 57467, 57487, 57493, 57503,  
         57527, 57529, 57557, 57559, 57571, 57587, 57593, 57601,  
         57637, 57641, 57649, 57653, 57667, 57679, 57689, 57697,  
         57709, 57713, 57719, 57727, 57731, 57737, 57751, 57773,  
         57781, 57787, 57791, 57793, 57803, 57809, 57829, 57839,  
         57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923,  
         57943, 57947, 57973, 57977, 57991, 58013, 58027, 58031,  
         58043, 58049, 58057, 58061, 58067, 58073, 58099, 58109,  
         58111, 58129, 58147, 58151, 58153, 58169, 58171, 58189,  
         58193, 58199, 58207, 58211, 58217, 58229, 58231, 58237,  
         58243, 58271, 58309, 58313, 58321, 58337, 58363, 58367,  
         58369, 58379, 58391, 58393, 58403, 58411, 58417, 58427,  
         58439, 58441, 58451, 58453, 58477, 58481, 58511, 58537,  
         58543, 58549, 58567, 58573, 58579, 58601, 58603, 58613,  
         58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711,  
         58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789,  
         58831, 58889, 58897, 58901, 58907, 58909, 58913, 58921,  
         58937, 58943, 58963, 58967, 58979, 58991, 58997, 59009,  
         59011, 59021, 59023, 59029, 59051, 59053, 59063, 59069,  
         59077, 59083, 59093, 59107, 59113, 59119, 59123, 59141,  
         59149, 59159, 59167, 59183, 59197, 59207, 59209, 59219,  
         59221, 59233, 59239, 59243, 59263, 59273, 59281, 59333,  
         59341, 59351, 59357, 59359, 59369, 59377, 59387, 59393,  
         59399, 59407, 59417, 59419, 59441, 59443, 59447, 59453,  
         59467, 59471, 59473, 59497, 59509, 59513, 59539, 59557,  
         59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629,  
         59651, 59659, 59663, 59669, 59671, 59693, 59699, 59707,  
         59723, 59729, 59743, 59747, 59753, 59771, 59779, 59791,  
         59797, 59809, 59833, 59863, 59879, 59887, 59921, 59929,  
         59951, 59957, 59971, 59981, 59999, 60013, 60017, 60029,  
         60037, 60041, 60077, 60083, 60089, 60091, 60101, 60103,  
         60107, 60127, 60133, 60139, 60149, 60161, 60167, 60169,  
         60209, 60217, 60223, 60251, 60257, 60259, 60271, 60289,  
         60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383,  
         60397, 60413, 60427, 60443, 60449, 60457, 60493, 60497,  
         60509, 60521, 60527, 60539, 60589, 60601, 60607, 60611,  
         60617, 60623, 60631, 60637, 60647, 60649, 60659, 60661,  
         60679, 60689, 60703, 60719, 60727, 60733, 60737, 60757,  
         60761, 60763, 60773, 60779, 60793, 60811, 60821, 60859,  
         60869, 60887, 60889, 60899, 60901, 60913, 60917, 60919,  
         60923, 60937, 60943, 60953, 60961, 61001, 61007, 61027,  
         61031, 61043, 61051, 61057, 61091, 61099, 61121, 61129,  
         61141, 61151, 61153, 61169, 61211, 61223, 61231, 61253,  
         61261, 61283, 61291, 61297, 61331, 61333, 61339, 61343,  
         61357, 61363, 61379, 61381, 61403, 61409, 61417, 61441,  
         61463, 61469, 61471, 61483, 61487, 61493, 61507, 61511,  
         61519, 61543, 61547, 61553, 61559, 61561, 61583, 61603,  
         61609, 61613, 61627, 61631, 61637, 61643, 61651, 61657,  
         61667, 61673, 61681, 61687, 61703, 61717, 61723, 61729,  
         61751, 61757, 61781, 61813, 61819, 61837, 61843, 61861,  
         61871, 61879, 61909, 61927, 61933, 61949, 61961, 61967,  
         61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039,  
         62047, 62053, 62057, 62071, 62081, 62099, 62119, 62129,  
         62131, 62137, 62141, 62143, 62171, 62189, 62191, 62201,  
         62207, 62213, 62219, 62233, 62273, 62297, 62299, 62303,  
         62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417,  
         62423, 62459, 62467, 62473, 62477, 62483, 62497, 62501,  
         62507, 62533, 62539, 62549, 62563, 62581, 62591, 62597,  
         62603, 62617, 62627, 62633, 62639, 62653, 62659, 62683,  
         62687, 62701, 62723, 62731, 62743, 62753, 62761, 62773,  
         62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873,  
         62897, 62903, 62921, 62927, 62929, 62939, 62969, 62971,  
         62981, 62983, 62987, 62989, 63029, 63031, 63059, 63067,  
         63073, 63079, 63097, 63103, 63113, 63127, 63131, 63149,  
         63179, 63197, 63199, 63211, 63241, 63247, 63277, 63281,  
         63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353,  
         63361, 63367, 63377, 63389, 63391, 63397, 63409, 63419,  
         63421, 63439, 63443, 63463, 63467, 63473, 63487, 63493,  
         63499, 63521, 63527, 63533, 63541, 63559, 63577, 63587,  
         63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647,  
         63649, 63659, 63667, 63671, 63689, 63691, 63697, 63703,  
         63709, 63719, 63727, 63737, 63743, 63761, 63773, 63781,  
         63793, 63799, 63803, 63809, 63823, 63839, 63841, 63853,  
         63857, 63863, 63901, 63907, 63913, 63929, 63949, 63977,  
         63997, 64007, 64013, 64019, 64033, 64037, 64063, 64067,  
         64081, 64091, 64109, 64123, 64151, 64153, 64157, 64171,  
         64187, 64189, 64217, 64223, 64231, 64237, 64271, 64279,  
         64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381,  
         64399, 64403, 64433, 64439, 64451, 64453, 64483, 64489,  
         64499, 64513, 64553, 64567, 64577, 64579, 64591, 64601,  
         64609, 64613, 64621, 64627, 64633, 64661, 64663, 64667,  
         64679, 64693, 64709, 64717, 64747, 64763, 64781, 64783,  
         64793, 64811, 64817, 64849, 64853, 64871, 64877, 64879,  
         64891, 64901, 64919, 64921, 64927, 64937, 64951, 64969,  
         64997, 65003, 65011, 65027, 65029, 65033, 65053, 65063,  
         65071, 65089, 65099, 65101, 65111, 65119, 65123, 65129,  
         65141, 65147, 65167, 65171, 65173, 65179, 65183, 65203,  
         65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309,  
         65323, 65327, 65353, 65357, 65371, 65381, 65393, 65407,  
         65413, 65419, 65423, 65437, 65447, 65449, 65479, 65497,  
         65519, 65521, 65537, 65539, 65543, 65551, 65557, 65563,  
         65579, 65581, 65587, 65599, 65609, 65617, 65629, 65633,  
         65647, 65651, 65657, 65677, 65687, 65699, 65701, 65707,  
         65713, 65717, 65719, 65729, 65731, 65761, 65777, 65789,  
         65809, 65827, 65831, 65837, 65839, 65843, 65851, 65867,  
         65881, 65899, 65921, 65927, 65929, 65951, 65957, 65963,  
         65981, 65983, 65993, 66029, 66037, 66041, 66047, 66067,  
         66071, 66083, 66089, 66103, 66107, 66109, 66137, 66161,  
         66169, 66173, 66179, 66191, 66221, 66239, 66271, 66293,  
         66301, 66337, 66343, 66347, 66359, 66361, 66373, 66377,  
         66383, 66403, 66413, 66431, 66449, 66457, 66463, 66467,  
         66491, 66499, 66509, 66523, 66529, 66533, 66541, 66553,  
         66569, 66571, 66587, 66593, 66601, 66617, 66629, 66643,  
         66653, 66683, 66697, 66701, 66713, 66721, 66733, 66739,  
         66749, 66751, 66763, 66791, 66797, 66809, 66821, 66841,  
         66851, 66853, 66863, 66877, 66883, 66889, 66919, 66923,  
         66931, 66943, 66947, 66949, 66959, 66973, 66977, 67003,  
         67021, 67033, 67043, 67049, 67057, 67061, 67073, 67079,  
         67103, 67121, 67129, 67139, 67141, 67153, 67157, 67169,  
         67181, 67187, 67189, 67211, 67213, 67217, 67219, 67231,  
         67247, 67261, 67271, 67273, 67289, 67307, 67339, 67343,  
         67349, 67369, 67391, 67399, 67409, 67411, 67421, 67427,  
         67429, 67433, 67447, 67453, 67477, 67481, 67489, 67493,  
         67499, 67511, 67523, 67531, 67537, 67547, 67559, 67567,  
         67577, 67579, 67589, 67601, 67607, 67619, 67631, 67651,  
         67679, 67699, 67709, 67723, 67733, 67741, 67751, 67757,  
         67759, 67763, 67777, 67783, 67789, 67801, 67807, 67819,  
         67829, 67843, 67853, 67867, 67883, 67891, 67901, 67927,  
         67931, 67933, 67939, 67943, 67957, 67961, 67967, 67979,  
         67987, 67993, 68023, 68041, 68053, 68059, 68071, 68087,  
         68099, 68111, 68113, 68141, 68147, 68161, 68171, 68207,  
         68209, 68213, 68219, 68227, 68239, 68261, 68279, 68281,  
         68311, 68329, 68351, 68371, 68389, 68399, 68437, 68443,  
         68447, 68449, 68473, 68477, 68483, 68489, 68491, 68501,  
         68507, 68521, 68531, 68539, 68543, 68567, 68581, 68597,  
         68611, 68633, 68639, 68659, 68669, 68683, 68687, 68699,  
         68711, 68713, 68729, 68737, 68743, 68749, 68767, 68771,  
         68777, 68791, 68813, 68819, 68821, 68863, 68879, 68881,  
         68891, 68897, 68899, 68903, 68909, 68917, 68927, 68947,  
         68963, 68993, 69001, 69011, 69019, 69029, 69031, 69061,  
         69067, 69073, 69109, 69119, 69127, 69143, 69149, 69151,  
         69163, 69191, 69193, 69197, 69203, 69221, 69233, 69239,  
         69247, 69257, 69259, 69263, 69313, 69317, 69337, 69341,  
         69371, 69379, 69383, 69389, 69401, 69403, 69427, 69431,  
         69439, 69457, 69463, 69467, 69473, 69481, 69491, 69493,  
         69497, 69499, 69539, 69557, 69593, 69623, 69653, 69661,  
         69677, 69691, 69697, 69709, 69737, 69739, 69761, 69763,  
         69767, 69779, 69809, 69821, 69827, 69829, 69833, 69847,  
         69857, 69859, 69877, 69899, 69911, 69929, 69931, 69941,  
         69959, 69991, 69997, 70001, 70003, 70009, 70019, 70039,  
         70051, 70061, 70067, 70079, 70099, 70111, 70117, 70121,  
         70123, 70139, 70141, 70157, 70163, 70177, 70181, 70183,  
         70199, 70201, 70207, 70223, 70229, 70237, 70241, 70249,  
         70271, 70289, 70297, 70309, 70313, 70321, 70327, 70351,  
         70373, 70379, 70381, 70393, 70423, 70429, 70439, 70451,  
         70457, 70459, 70481, 70487, 70489, 70501, 70507, 70529,  
         70537, 70549, 70571, 70573, 70583, 70589, 70607, 70619,  
         70621, 70627, 70639, 70657, 70663, 70667, 70687, 70709,  
         70717, 70729, 70753, 70769, 70783, 70793, 70823, 70841,  
         70843, 70849, 70853, 70867, 70877, 70879, 70891, 70901,  
         70913, 70919, 70921, 70937, 70949, 70951, 70957, 70969,  
         70979, 70981, 70991, 70997, 70999, 71011, 71023, 71039,  
         71059, 71069, 71081, 71089, 71119, 71129, 71143, 71147,  
         71153, 71161, 71167, 71171, 71191, 71209, 71233, 71237,  
         71249, 71257, 71261, 71263, 71287, 71293, 71317, 71327,  
         71329, 71333, 71339, 71341, 71347, 71353, 71359, 71363,  
         71387, 71389, 71399, 71411, 71413, 71419, 71429, 71437,  
         71443, 71453, 71471, 71473, 71479, 71483, 71503, 71527,  
         71537, 71549, 71551, 71563, 71569, 71593, 71597, 71633,  
         71647, 71663, 71671, 71693, 71699, 71707, 71711, 71713,  
         71719, 71741, 71761, 71777, 71789, 71807, 71809, 71821,  
         71837, 71843, 71849, 71861, 71867, 71879, 71881, 71887,  
         71899, 71909, 71917, 71933, 71941, 71947, 71963, 71971,  
         71983, 71987, 71993, 71999, 72019, 72031, 72043, 72047,  
         72053, 72073, 72077, 72089, 72091, 72101, 72103, 72109,  
         72139, 72161, 72167, 72169, 72173, 72211, 72221, 72223,  
         72227, 72229, 72251, 72253, 72269, 72271, 72277, 72287,  
         72307, 72313, 72337, 72341, 72353, 72367, 72379, 72383,  
         72421, 72431, 72461, 72467, 72469, 72481, 72493, 72497,  
         72503, 72533, 72547, 72551, 72559, 72577, 72613, 72617,  
         72623, 72643, 72647, 72649, 72661, 72671, 72673, 72679,  
         72689, 72701, 72707, 72719, 72727, 72733, 72739, 72763,  
         72767, 72797, 72817, 72823, 72859, 72869, 72871, 72883,  
         72889, 72893, 72901, 72907, 72911, 72923, 72931, 72937,  
         72949, 72953, 72959, 72973, 72977, 72997, 73009, 73013,  
         73019, 73037, 73039, 73043, 73061, 73063, 73079, 73091,  
         73121, 73127, 73133, 73141, 73181, 73189, 73237, 73243,  
         73259, 73277, 73291, 73303, 73309, 73327, 73331, 73351,  
         73361, 73363, 73369, 73379, 73387, 73417, 73421, 73433,  
         73453, 73459, 73471, 73477, 73483, 73517, 73523, 73529,  
         73547, 73553, 73561, 73571, 73583, 73589, 73597, 73607,  
         73609, 73613, 73637, 73643, 73651, 73673, 73679, 73681,  
         73693, 73699, 73709, 73721, 73727, 73751, 73757, 73771,  
         73783, 73819, 73823, 73847, 73849, 73859, 73867, 73877,  
         73883, 73897, 73907, 73939, 73943, 73951, 73961, 73973,  
         73999, 74017, 74021, 74027, 74047, 74051, 74071, 74077,  
         74093, 74099, 74101, 74131, 74143, 74149, 74159, 74161,  
         74167, 74177, 74189, 74197, 74201, 74203, 74209, 74219,  
         74231, 74257, 74279, 74287, 74293, 74297, 74311, 74317,  
         74323, 74353, 74357, 74363, 74377, 74381, 74383, 74411,  
         74413, 74419, 74441, 74449, 74453, 74471, 74489, 74507,  
         74509, 74521, 74527, 74531, 74551, 74561, 74567, 74573,  
         74587, 74597, 74609, 74611, 74623, 74653, 74687, 74699,  
         74707, 74713, 74717, 74719, 74729, 74731, 74747, 74759,  
         74761, 74771, 74779, 74797, 74821, 74827, 74831, 74843,  
         74857, 74861, 74869, 74873, 74887, 74891, 74897, 74903,  
         74923, 74929, 74933, 74941, 74959, 75011, 75013, 75017,  
         75029, 75037, 75041, 75079, 75083, 75109, 75133, 75149,  
         75161, 75167, 75169, 75181, 75193, 75209, 75211, 75217,  
         75223, 75227, 75239, 75253, 75269, 75277, 75289, 75307,  
         75323, 75329, 75337, 75347, 75353, 75367, 75377, 75389,  
         75391, 75401, 75403, 75407, 75431, 75437, 75479, 75503,  
         75511, 75521, 75527, 75533, 75539, 75541, 75553, 75557,  
         75571, 75577, 75583, 75611, 75617, 75619, 75629, 75641,  
         75653, 75659, 75679, 75683, 75689, 75703, 75707, 75709,  
         75721, 75731, 75743, 75767, 75773, 75781, 75787, 75793,  
         75797, 75821, 75833, 75853, 75869, 75883, 75913, 75931,  
         75937, 75941, 75967, 75979, 75983, 75989, 75991, 75997,  
         76001, 76003, 76031, 76039, 76079, 76081, 76091, 76099,  
         76103, 76123, 76129, 76147, 76157, 76159, 76163, 76207,  
         76213, 76231, 76243, 76249, 76253, 76259, 76261, 76283,  
         76289, 76303, 76333, 76343, 76367, 76369, 76379, 76387,  
         76403, 76421, 76423, 76441, 76463, 76471, 76481, 76487,  
         76493, 76507, 76511, 76519, 76537, 76541, 76543, 76561,  
         76579, 76597, 76603, 76607, 76631, 76649, 76651, 76667,  
         76673, 76679, 76697, 76717, 76733, 76753, 76757, 76771,  
         76777, 76781, 76801, 76819, 76829, 76831, 76837, 76847,  
         76871, 76873, 76883, 76907, 76913, 76919, 76943, 76949,  
         76961, 76963, 76991, 77003, 77017, 77023, 77029, 77041,  
         77047, 77069, 77081, 77093, 77101, 77137, 77141, 77153,  
         77167, 77171, 77191, 77201, 77213, 77237, 77239, 77243,  
         77249, 77261, 77263, 77267, 77269, 77279, 77291, 77317,  
         77323, 77339, 77347, 77351, 77359, 77369, 77377, 77383,  
         77417, 77419, 77431, 77447, 77471, 77477, 77479, 77489,  
         77491, 77509, 77513, 77521, 77527, 77543, 77549, 77551,  
         77557, 77563, 77569, 77573, 77587, 77591, 77611, 77617,  
         77621, 77641, 77647, 77659, 77681, 77687, 77689, 77699,  
         77711, 77713, 77719, 77723, 77731, 77743, 77747, 77761,  
         77773, 77783, 77797, 77801, 77813, 77839, 77849, 77863,  
         77867, 77893, 77899, 77929, 77933, 77951, 77969, 77977,  
         77983, 77999, 78007, 78017, 78031, 78041, 78049, 78059,  
         78079, 78101, 78121, 78137, 78139, 78157, 78163, 78167,  
         78173, 78179, 78191, 78193, 78203, 78229, 78233, 78241,  
         78259, 78277, 78283, 78301, 78307, 78311, 78317, 78341,  
         78347, 78367, 78401, 78427, 78437, 78439, 78467, 78479,  
         78487, 78497, 78509, 78511, 78517, 78539, 78541, 78553,  
         78569, 78571, 78577, 78583, 78593, 78607, 78623, 78643,  
         78649, 78653, 78691, 78697, 78707, 78713, 78721, 78737,  
         78779, 78781, 78787, 78791, 78797, 78803, 78809, 78823,  
         78839, 78853, 78857, 78877, 78887, 78889, 78893, 78901,  
         78919, 78929, 78941, 78977, 78979, 78989, 79031, 79039,  
         79043, 79063, 79087, 79103, 79111, 79133, 79139, 79147,  
         79151, 79153, 79159, 79181, 79187, 79193, 79201, 79229,  
         79231, 79241, 79259, 79273, 79279, 79283, 79301, 79309,  
         79319, 79333, 79337, 79349, 79357, 79367, 79379, 79393,  
         79397, 79399, 79411, 79423, 79427, 79433, 79451, 79481,  
         79493, 79531, 79537, 79549, 79559, 79561, 79579, 79589,  
         79601, 79609, 79613, 79621, 79627, 79631, 79633, 79657,  
         79669, 79687, 79691, 79693, 79697, 79699, 79757, 79769,  
         79777, 79801, 79811, 79813, 79817, 79823, 79829, 79841,  
         79843, 79847, 79861, 79867, 79873, 79889, 79901, 79903,  
         79907, 79939, 79943, 79967, 79973, 79979, 79987, 79997,  
         79999, 80021, 80039, 80051, 80071, 80077, 80107, 80111,  
         80141, 80147, 80149, 80153, 80167, 80173, 80177, 80191,  
         80207, 80209, 80221, 80231, 80233, 80239, 80251, 80263,  
         80273, 80279, 80287, 80309, 80317, 80329, 80341, 80347,  
         80363, 80369, 80387, 80407, 80429, 80447, 80449, 80471,  
         80473, 80489, 80491, 80513, 80527, 80537, 80557, 80567,  
         80599, 80603, 80611, 80621, 80627, 80629, 80651, 80657,  
         80669, 80671, 80677, 80681, 80683, 80687, 80701, 80713,  
         80737, 80747, 80749, 80761, 80777, 80779, 80783, 80789,  
         80803, 80809, 80819, 80831, 80833, 80849, 80863, 80897,  
         80909, 80911, 80917, 80923, 80929, 80933, 80953, 80963,  
         80989, 81001, 81013, 81017, 81019, 81023, 81031, 81041,  
         81043, 81047, 81049, 81071, 81077, 81083, 81097, 81101,  
         81119, 81131, 81157, 81163, 81173, 81181, 81197, 81199,  
         81203, 81223, 81233, 81239, 81281, 81283, 81293, 81299,  
         81307, 81331, 81343, 81349, 81353, 81359, 81371, 81373,  
         81401, 81409, 81421, 81439, 81457, 81463, 81509, 81517,  
         81527, 81533, 81547, 81551, 81553, 81559, 81563, 81569,  
         81611, 81619, 81629, 81637, 81647, 81649, 81667, 81671,  
         81677, 81689, 81701, 81703, 81707, 81727, 81737, 81749,  
         81761, 81769, 81773, 81799, 81817, 81839, 81847, 81853,  
         81869, 81883, 81899, 81901, 81919, 81929, 81931, 81937,  
         81943, 81953, 81967, 81971, 81973, 82003, 82007, 82009,  
         82013, 82021, 82031, 82037, 82039, 82051, 82067, 82073,  
         82129, 82139, 82141, 82153, 82163, 82171, 82183, 82189,  
         82193, 82207, 82217, 82219, 82223, 82231, 82237, 82241,  
         82261, 82267, 82279, 82301, 82307, 82339, 82349, 82351,  
         82361, 82373, 82387, 82393, 82421, 82457, 82463, 82469,  
         82471, 82483, 82487, 82493, 82499, 82507, 82529, 82531,  
         82549, 82559, 82561, 82567, 82571, 82591, 82601, 82609,  
         82613, 82619, 82633, 82651, 82657, 82699, 82721, 82723,  
         82727, 82729, 82757, 82759, 82763, 82781, 82787, 82793,  
         82799, 82811, 82813, 82837, 82847, 82883, 82889, 82891,  
         82903, 82913, 82939, 82963, 82981, 82997, 83003, 83009,  
         83023, 83047, 83059, 83063, 83071, 83077, 83089, 83093,  
         83101, 83117, 83137, 83177, 83203, 83207, 83219, 83221,  
         83227, 83231, 83233, 83243, 83257, 83267, 83269, 83273,  
         83299, 83311, 83339, 83341, 83357, 83383, 83389, 83399,  
         83401, 83407, 83417, 83423, 83431, 83437, 83443, 83449,  
         83459, 83471, 83477, 83497, 83537, 83557, 83561, 83563,  
         83579, 83591, 83597, 83609, 83617, 83621, 83639, 83641,  
         83653, 83663, 83689, 83701, 83717, 83719, 83737, 83761,  
         83773, 83777, 83791, 83813, 83833, 83843, 83857, 83869,  
         83873, 83891, 83903, 83911, 83921, 83933, 83939, 83969,  
         83983, 83987, 84011, 84017, 84047, 84053, 84059, 84061,  
         84067, 84089, 84121, 84127, 84131, 84137, 84143, 84163,  
         84179, 84181, 84191, 84199, 84211, 84221, 84223, 84229,  
         84239, 84247, 84263, 84299, 84307, 84313, 84317, 84319,  
         84347, 84349, 84377, 84389, 84391, 84401, 84407, 84421,  
         84431, 84437, 84443, 84449, 84457, 84463, 84467, 84481,  
         84499, 84503, 84509, 84521, 84523, 84533, 84551, 84559,  
         84589, 84629, 84631, 84649, 84653, 84659, 84673, 84691,  
         84697, 84701, 84713, 84719, 84731, 84737, 84751, 84761,  
         84787, 84793, 84809, 84811, 84827, 84857, 84859, 84869,  
         84871, 84913, 84919, 84947, 84961, 84967, 84977, 84979,  
         84991, 85009, 85021, 85027, 85037, 85049, 85061, 85081,  
         85087, 85091, 85093, 85103, 85109, 85121, 85133, 85147,  
         85159, 85193, 85199, 85201, 85213, 85223, 85229, 85237,  
         85243, 85247, 85259, 85297, 85303, 85313, 85331, 85333,  
         85361, 85363, 85369, 85381, 85411, 85427, 85429, 85439,  
         85447, 85451, 85453, 85469, 85487, 85513, 85517, 85523,  
         85531, 85549, 85571, 85577, 85597, 85601, 85607, 85619,  
         85621, 85627, 85639, 85643, 85661, 85667, 85669, 85691,  
         85703, 85711, 85717, 85733, 85751, 85781, 85793, 85817,  
         85819, 85829, 85831, 85837, 85843, 85847, 85853, 85889,  
         85903, 85909, 85931, 85933, 85991, 85999, 86011, 86017,  
         86027, 86029, 86069, 86077, 86083, 86111, 86113, 86117,  
         86131, 86137, 86143, 86161, 86171, 86179, 86183, 86197,  
         86201, 86209, 86239, 86243, 86249, 86257, 86263, 86269,  
         86287, 86291, 86293, 86297, 86311, 86323, 86341, 86351,  
         86353, 86357, 86369, 86371, 86381, 86389, 86399, 86413,  
         86423, 86441, 86453, 86461, 86467, 86477, 86491, 86501,  
         86509, 86531, 86533, 86539, 86561, 86573, 86579, 86587,  
         86599, 86627, 86629, 86677, 86689, 86693, 86711, 86719,  
         86729, 86743, 86753, 86767, 86771, 86783, 86813, 86837,  
         86843, 86851, 86857, 86861, 86869, 86923, 86927, 86929,  
         86939, 86951, 86959, 86969, 86981, 86993, 87011, 87013,  
         87037, 87041, 87049, 87071, 87083, 87103, 87107, 87119,  
         87121, 87133, 87149, 87151, 87179, 87181, 87187, 87211,  
         87221, 87223, 87251, 87253, 87257, 87277, 87281, 87293,  
         87299, 87313, 87317, 87323, 87337, 87359, 87383, 87403,  
         87407, 87421, 87427, 87433, 87443, 87473, 87481, 87491,  
         87509, 87511, 87517, 87523, 87539, 87541, 87547, 87553,  
         87557, 87559, 87583, 87587, 87589, 87613, 87623, 87629,  
         87631, 87641, 87643, 87649, 87671, 87679, 87683, 87691,  
         87697, 87701, 87719, 87721, 87739, 87743, 87751, 87767,  
         87793, 87797, 87803, 87811, 87833, 87853, 87869, 87877,  
         87881, 87887, 87911, 87917, 87931, 87943, 87959, 87961,  
         87973, 87977, 87991, 88001, 88003, 88007, 88019, 88037,  
         88069, 88079, 88093, 88117, 88129, 88169, 88177, 88211,  
         88223, 88237, 88241, 88259, 88261, 88289, 88301, 88321,  
         88327, 88337, 88339, 88379, 88397, 88411, 88423, 88427,  
         88463, 88469, 88471, 88493, 88499, 88513, 88523, 88547,  
         88589, 88591, 88607, 88609, 88643, 88651, 88657, 88661,  
         88663, 88667, 88681, 88721, 88729, 88741, 88747, 88771,  
         88789, 88793, 88799, 88801, 88807, 88811, 88813, 88817,  
         88819, 88843, 88853, 88861, 88867, 88873, 88883, 88897,  
         88903, 88919, 88937, 88951, 88969, 88993, 88997, 89003,  
         89009, 89017, 89021, 89041, 89051, 89057, 89069, 89071,  
         89083, 89087, 89101, 89107, 89113, 89119, 89123, 89137,  
         89153, 89189, 89203, 89209, 89213, 89227, 89231, 89237,  
         89261, 89269, 89273, 89293, 89303, 89317, 89329, 89363,  
         89371, 89381, 89387, 89393, 89399, 89413, 89417, 89431,  
         89443, 89449, 89459, 89477, 89491, 89501, 89513, 89519,  
         89521, 89527, 89533, 89561, 89563, 89567, 89591, 89597,  
         89599, 89603, 89611, 89627, 89633, 89653, 89657, 89659,  
         89669, 89671, 89681, 89689, 89753, 89759, 89767, 89779,  
         89783, 89797, 89809, 89819, 89821, 89833, 89839, 89849,  
         89867, 89891, 89897, 89899, 89909, 89917, 89923, 89939,  
         89959, 89963, 89977, 89983, 89989, 90001, 90007, 90011,  
         90017, 90019, 90023, 90031, 90053, 90059, 90067, 90071,  
         90073, 90089, 90107, 90121, 90127, 90149, 90163, 90173,  
         90187, 90191, 90197, 90199, 90203, 90217, 90227, 90239,  
         90247, 90263, 90271, 90281, 90289, 90313, 90353, 90359,  
         90371, 90373, 90379, 90397, 90401, 90403, 90407, 90437,  
         90439, 90469, 90473, 90481, 90499, 90511, 90523, 90527,  
         90529, 90533, 90547, 90583, 90599, 90617, 90619, 90631,  
         90641, 90647, 90659, 90677, 90679, 90697, 90703, 90709,  
         90731, 90749, 90787, 90793, 90803, 90821, 90823, 90833,  
         90841, 90847, 90863, 90887, 90901, 90907, 90911, 90917,  
         90931, 90947, 90971, 90977, 90989, 90997, 91009, 91019,  
         91033, 91079, 91081, 91097, 91099, 91121, 91127, 91129,  
         91139, 91141, 91151, 91153, 91159, 91163, 91183, 91193,  
         91199, 91229, 91237, 91243, 91249, 91253, 91283, 91291,  
         91297, 91303, 91309, 91331, 91367, 91369, 91373, 91381,  
         91387, 91393, 91397, 91411, 91423, 91433, 91453, 91457,  
         91459, 91463, 91493, 91499, 91513, 91529, 91541, 91571,  
         91573, 91577, 91583, 91591, 91621, 91631, 91639, 91673,  
         91691, 91703, 91711, 91733, 91753, 91757, 91771, 91781,  
         91801, 91807, 91811, 91813, 91823, 91837, 91841, 91867,  
         91873, 91909, 91921, 91939, 91943, 91951, 91957, 91961,  
         91967, 91969, 91997, 92003, 92009, 92033, 92041, 92051,  
         92077, 92083, 92107, 92111, 92119, 92143, 92153, 92173,  
         92177, 92179, 92189, 92203, 92219, 92221, 92227, 92233,  
         92237, 92243, 92251, 92269, 92297, 92311, 92317, 92333,  
         92347, 92353, 92357, 92363, 92369, 92377, 92381, 92383,  
         92387, 92399, 92401, 92413, 92419, 92431, 92459, 92461,  
         92467, 92479, 92489, 92503, 92507, 92551, 92557, 92567,  
         92569, 92581, 92593, 92623, 92627, 92639, 92641, 92647,  
         92657, 92669, 92671, 92681, 92683, 92693, 92699, 92707,  
         92717, 92723, 92737, 92753, 92761, 92767, 92779, 92789,  
         92791, 92801, 92809, 92821, 92831, 92849, 92857, 92861,  
         92863, 92867, 92893, 92899, 92921, 92927, 92941, 92951,  
         92957, 92959, 92987, 92993, 93001, 93047, 93053, 93059,  
         93077, 93083, 93089, 93097, 93103, 93113, 93131, 93133,  
         93139, 93151, 93169, 93179, 93187, 93199, 93229, 93239,  
         93241, 93251, 93253, 93257, 93263, 93281, 93283, 93287,  
         93307, 93319, 93323, 93329, 93337, 93371, 93377, 93383,  
         93407, 93419, 93427, 93463, 93479, 93481, 93487, 93491,  
         93493, 93497, 93503, 93523, 93529, 93553, 93557, 93559,  
         93563, 93581, 93601, 93607, 93629, 93637, 93683, 93701,  
         93703, 93719, 93739, 93761, 93763, 93787, 93809, 93811,  
         93827, 93851, 93871, 93887, 93889, 93893, 93901, 93911,  
         93913, 93923, 93937, 93941, 93949, 93967, 93971, 93979,  
         93983, 93997, 94007, 94009, 94033, 94049, 94057, 94063,  
         94079, 94099, 94109, 94111, 94117, 94121, 94151, 94153,  
         94169, 94201, 94207, 94219, 94229, 94253, 94261, 94273,  
         94291, 94307, 94309, 94321, 94327, 94331, 94343, 94349,  
         94351, 94379, 94397, 94399, 94421, 94427, 94433, 94439,  
         94441, 94447, 94463, 94477, 94483, 94513, 94529, 94531,  
         94541, 94543, 94547, 94559, 94561, 94573, 94583, 94597,  
         94603, 94613, 94621, 94649, 94651, 94687, 94693, 94709,  
         94723, 94727, 94747, 94771, 94777, 94781, 94789, 94793,  
         94811, 94819, 94823, 94837, 94841, 94847, 94849, 94873,  
         94889, 94903, 94907, 94933, 94949, 94951, 94961, 94993,  
         94999, 95003, 95009, 95021, 95027, 95063, 95071, 95083,  
         95087, 95089, 95093, 95101, 95107, 95111, 95131, 95143,  
         95153, 95177, 95189, 95191, 95203, 95213, 95219, 95231,  
         95233, 95239, 95257, 95261, 95267, 95273, 95279, 95287,  
         95311, 95317, 95327, 95339, 95369, 95383, 95393, 95401,  
         95413, 95419, 95429, 95441, 95443, 95461, 95467, 95471,  
         95479, 95483, 95507, 95527, 95531, 95539, 95549, 95561,  
         95569, 95581, 95597, 95603, 95617, 95621, 95629, 95633,  
         95651, 95701, 95707, 95713, 95717, 95723, 95731, 95737,  
         95747, 95773, 95783, 95789, 95791, 95801, 95803, 95813,  
         95819, 95857, 95869, 95873, 95881, 95891, 95911, 95917,  
         95923, 95929, 95947, 95957, 95959, 95971, 95987, 95989,  
         96001, 96013, 96017, 96043, 96053, 96059, 96079, 96097,  
         96137, 96149, 96157, 96167, 96179, 96181, 96199, 96211,  
         96221, 96223, 96233, 96259, 96263, 96269, 96281, 96289,  
         96293, 96323, 96329, 96331, 96337, 96353, 96377, 96401,  
         96419, 96431, 96443, 96451, 96457, 96461, 96469, 96479,  
         96487, 96493, 96497, 96517, 96527, 96553, 96557, 96581,  
         96587, 96589, 96601, 96643, 96661, 96667, 96671, 96697,  
         96703, 96731, 96737, 96739, 96749, 96757, 96763, 96769,  
         96779, 96787, 96797, 96799, 96821, 96823, 96827, 96847,  
         96851, 96857, 96893, 96907, 96911, 96931, 96953, 96959,  
         96973, 96979, 96989, 96997, 97001, 97003, 97007, 97021,  
         97039, 97073, 97081, 97103, 97117, 97127, 97151, 97157,  
         97159, 97169, 97171, 97177, 97187, 97213, 97231, 97241,  
         97259, 97283, 97301, 97303, 97327, 97367, 97369, 97373,  
         97379, 97381, 97387, 97397, 97423, 97429, 97441, 97453,  
         97459, 97463, 97499, 97501, 97511, 97523, 97547, 97549,  
         97553, 97561, 97571, 97577, 97579, 97583, 97607, 97609,  
         97613, 97649, 97651, 97673, 97687, 97711, 97729, 97771,  
         97777, 97787, 97789, 97813, 97829, 97841, 97843, 97847,  
         97849, 97859, 97861, 97871, 97879, 97883, 97919, 97927,  
         97931, 97943, 97961, 97967, 97973, 97987, 98009, 98011,  
         98017, 98041, 98047, 98057, 98081, 98101, 98123, 98129,  
         98143, 98179, 98207, 98213, 98221, 98227, 98251, 98257,  
         98269, 98297, 98299, 98317, 98321, 98323, 98327, 98347,  
         98369, 98377, 98387, 98389, 98407, 98411, 98419, 98429,  
         98443, 98453, 98459, 98467, 98473, 98479, 98491, 98507,  
         98519, 98533, 98543, 98561, 98563, 98573, 98597, 98621,  
         98627, 98639, 98641, 98663, 98669, 98689, 98711, 98713,  
         98717, 98729, 98731, 98737, 98773, 98779, 98801, 98807,  
         98809, 98837, 98849, 98867, 98869, 98873, 98887, 98893,  
         98897, 98899, 98909, 98911, 98927, 98929, 98939, 98947,  
         98953, 98963, 98981, 98993, 98999, 99013, 99017, 99023,  
         99041, 99053, 99079, 99083, 99089, 99103, 99109, 99119,  
         99131, 99133, 99137, 99139, 99149, 99173, 99181, 99191,  
         99223, 99233, 99241, 99251, 99257, 99259, 99277, 99289,  
         99317, 99347, 99349, 99367, 99371, 99377, 99391, 99397,  
         99401, 99409, 99431, 99439, 99469, 99487, 99497, 99523,  
         99527, 99529, 99551, 99559, 99563, 99571, 99577, 99581,  
         99607, 99611, 99623, 99643, 99661, 99667, 99679, 99689,  
         99707, 99709, 99713, 99719, 99721, 99733, 99761, 99767,  
         99787, 99793, 99809, 99817, 99823, 99829, 99833, 99839,  
         99859, 99871, 99877, 99881, 99901, 99907, 99923, 99929,  
         99961, 99971, 99989, 99991, 100003, 100019, 100043, 100049,  
         100057, 100069, 100103, 100109, 100129, 100151, 100153, 100169,  
         100183, 100189, 100193, 100207, 100213, 100237, 100267, 100271,  
         100279, 100291, 100297, 100313, 100333, 100343, 100357, 100361,  
         100363, 100379, 100391, 100393, 100403, 100411, 100417, 100447,  
         100459, 100469, 100483, 100493, 100501, 100511, 100517, 100519,  
         100523, 100537, 100547, 100549, 100559, 100591, 100609, 100613,  
         100621, 100649, 100669, 100673, 100693, 100699, 100703, 100733,  
         100741, 100747, 100769, 100787, 100799, 100801, 100811, 100823,  
         100829, 100847, 100853, 100907, 100913, 100927, 100931, 100937,  
         100943, 100957, 100981, 100987, 100999, 101009, 101021, 101027,  
         101051, 101063, 101081, 101089, 101107, 101111, 101113, 101117,  
         101119, 101141, 101149, 101159, 101161, 101173, 101183, 101197,  
         101203, 101207, 101209, 101221, 101267, 101273, 101279, 101281,  
         101287, 101293, 101323, 101333, 101341, 101347, 101359, 101363,  
         101377, 101383, 101399, 101411, 101419, 101429, 101449, 101467,  
         101477, 101483, 101489, 101501, 101503, 101513, 101527, 101531,  
         101533, 101537, 101561, 101573, 101581, 101599, 101603, 101611,  
         101627, 101641, 101653, 101663, 101681, 101693, 101701, 101719,  
         101723, 101737, 101741, 101747, 101749, 101771, 101789, 101797,  
         101807, 101833, 101837, 101839, 101863, 101869, 101873, 101879,  
         101891, 101917, 101921, 101929, 101939, 101957, 101963, 101977,  
         101987, 101999, 102001, 102013, 102019, 102023, 102031, 102043,  
         102059, 102061, 102071, 102077, 102079, 102101, 102103, 102107,  
         102121, 102139, 102149, 102161, 102181, 102191, 102197, 102199,  
         102203, 102217, 102229, 102233, 102241, 102251, 102253, 102259,  
         102293, 102299, 102301, 102317, 102329, 102337, 102359, 102367,  
         102397, 102407, 102409, 102433, 102437, 102451, 102461, 102481,  
         102497, 102499, 102503, 102523, 102533, 102539, 102547, 102551,  
         102559, 102563, 102587, 102593, 102607, 102611, 102643, 102647,  
         102653, 102667, 102673, 102677, 102679, 102701, 102761, 102763,  
         102769, 102793, 102797, 102811, 102829, 102841, 102859, 102871,  
         102877, 102881, 102911, 102913, 102929, 102931, 102953, 102967,  
         102983, 103001, 103007, 103043, 103049, 103067, 103069, 103079,  
         103087, 103091, 103093, 103099, 103123, 103141, 103171, 103177,  
         103183, 103217, 103231, 103237, 103289, 103291, 103307, 103319,  
         103333, 103349, 103357, 103387, 103391, 103393, 103399, 103409,  
         103421, 103423, 103451, 103457, 103471, 103483, 103511, 103529,  
         103549, 103553, 103561, 103567, 103573, 103577, 103583, 103591,  
         103613, 103619, 103643, 103651, 103657, 103669, 103681, 103687,  
         103699, 103703, 103723, 103769, 103787, 103801, 103811, 103813,  
         103837, 103841, 103843, 103867, 103889, 103903, 103913, 103919,  
         103951, 103963, 103967, 103969, 103979, 103981, 103991, 103993,  
         103997, 104003, 104009, 104021, 104033, 104047, 104053, 104059,  
         104087, 104089, 104107, 104113, 104119, 104123, 104147, 104149,  
         104161, 104173, 104179, 104183, 104207, 104231, 104233, 104239,  
         104243, 104281, 104287, 104297, 104309, 104311, 104323, 104327,  
         104347, 104369, 104381, 104383, 104393, 104399, 104417, 104459,  
         104471, 104473, 104479, 104491, 104513, 104527, 104537, 104543,  
         104549, 104551, 104561, 104579, 104593, 104597, 104623, 104639,  
         104651, 104659, 104677, 104681, 104683, 104693, 104701, 104707,  
         104711, 104717, 104723, 104729 
     );
    
    
    // loop through while dividing by each prime to find multiplier
    $div = 0;
    $count = 0;
    
    // loop
    do {
        
        // divid
        $div = $num / $primes[$count];
        
        // compare result to rounded to see if we have an integer
        if( $div == round( $div ) && $div != 1 )
            return 'not prime, divisible by '. $primes[$count];      
            
    } while ( $count < count( $primes ) && $primes[$count++] <= $sr );  
      
    // the number is prime.        
    return true;    
 
}
        
?>
Jul 12, 2011
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