/******************************************************************************
*									      *
*  PRIME LOOK-UP TABLE							      *
*  03/21/16 (dkc)							      *
*									      *
*  This table consists of primes of the form p*k+1 for p=3.		      *
*									      *
******************************************************************************/
unsigned int table3[4784]={
 7, 
 13, 
 19, 
 31, 
 37, 
 43, 
 61, 
 67, 
 73, 
 79, 
 97, 
 103, 
 109, 
 127, 
 139, 
 151, 
 157, 
 163, 
 181, 
 193, 
 199, 
 211, 
 223, 
 229, 
 241, 
 271, 
 277, 
 283, 
 307, 
 313, 
 331, 
 337, 
 349, 
 367, 
 373, 
 379, 
 397, 
 409, 
 421, 
 433, 
 439, 
 457, 
 463, 
 487, 
 499, 
 523, 
 541, 
 547, 
 571, 
 577, 
 601, 
 607, 
 613, 
 619, 
 631, 
 643, 
 661, 
 673, 
 691, 
 709, 
 727, 
 733, 
 739, 
 751, 
 757, 
 769, 
 787, 
 811, 
 823, 
 829, 
 853, 
 859, 
 877, 
 883, 
 907, 
 919, 
 937, 
 967, 
 991, 
 997, 
 1009, 
 1021, 
 1033, 
 1039, 
 1051, 
 1063, 
 1069, 
 1087, 
 1093, 
 1117, 
 1123, 
 1129, 
 1153, 
 1171, 
 1201, 
 1213, 
 1231, 
 1237, 
 1249, 
 1279, 
 1291, 
 1297, 
 1303, 
 1321, 
 1327, 
 1381, 
 1399, 
 1423, 
 1429, 
 1447, 
 1453, 
 1459, 
 1471, 
 1483, 
 1489, 
 1531, 
 1543, 
 1549, 
 1567, 
 1579, 
 1597, 
 1609, 
 1621, 
 1627, 
 1657, 
 1663, 
 1669, 
 1693, 
 1699, 
 1723, 
 1741, 
 1747, 
 1753, 
 1759, 
 1777, 
 1783, 
 1789, 
 1801, 
 1831, 
 1861, 
 1867, 
 1873, 
 1879, 
 1933, 
 1951, 
 1987, 
 1993, 
 1999, 
 2011, 
 2017, 
 2029, 
 2053, 
 2083, 
 2089, 
 2113, 
 2131, 
 2137, 
 2143, 
 2161, 
 2179, 
 2203, 
 2221, 
 2239, 
 2251, 
 2269, 
 2281, 
 2287, 
 2293, 
 2311, 
 2341, 
 2347, 
 2371, 
 2377, 
 2383, 
 2389, 
 2437, 
 2467, 
 2473, 
 2503, 
 2521, 
 2539, 
 2551, 
 2557, 
 2593, 
 2617, 
 2647, 
 2659, 
 2671, 
 2677, 
 2683, 
 2689, 
 2707, 
 2713, 
 2719, 
 2731, 
 2749, 
 2767, 
 2791, 
 2797, 
 2803, 
 2833, 
 2851, 
 2857, 
 2887, 
 2917, 
 2953, 
 2971, 
 3001, 
 3019, 
 3037, 
 3049, 
 3061, 
 3067, 
 3079, 
 3109, 
 3121, 
 3163, 
 3169, 
 3181, 
 3187, 
 3217, 
 3229, 
 3253, 
 3259, 
 3271, 
 3301, 
 3307, 
 3313, 
 3319, 
 3331, 
 3343, 
 3361, 
 3373, 
 3391, 
 3433, 
 3457, 
 3463, 
 3469, 
 3499, 
 3511, 
 3517, 
 3529, 
 3541, 
 3547, 
 3559, 
 3571, 
 3583, 
 3607, 
 3613, 
 3631, 
 3637, 
 3643, 
 3673, 
 3691, 
 3697, 
 3709, 
 3727, 
 3733, 
 3739, 
 3769, 
 3793, 
 3823, 
 3847, 
 3853, 
 3877, 
 3889, 
 3907, 
 3919, 
 3931, 
 3943, 
 3967, 
 4003, 
 4021, 
 4027, 
 4051, 
 4057, 
 4093, 
 4099, 
 4111, 
 4129, 
 4153, 
 4159, 
 4177, 
 4201, 
 4219, 
 4231, 
 4243, 
 4261, 
 4273, 
 4297, 
 4327, 
 4339, 
 4357, 
 4363, 
 4423, 
 4441, 
 4447, 
 4483, 
 4507, 
 4513, 
 4519, 
 4549, 
 4561, 
 4567, 
 4591, 
 4597, 
 4603, 
 4621, 
 4639, 
 4651, 
 4657, 
 4663, 
 4723, 
 4729, 
 4759, 
 4783, 
 4789, 
 4801, 
 4813, 
 4831, 
 4861, 
 4903, 
 4909, 
 4933, 
 4951, 
 4957, 
 4969, 
 4987, 
 4993, 
 4999, 
 5011, 
 5023, 
 5059, 
 5077, 
 5101, 
 5107, 
 5113, 
 5119, 
 5167, 
 5179, 
 5197, 
 5209, 
 5227, 
 5233, 
 5281, 
 5323, 
 5347, 
 5407, 
 5413, 
 5419, 
 5431, 
 5437, 
 5443, 
 5449, 
 5479, 
 5503, 
 5521, 
 5527, 
 5557, 
 5563, 
 5569, 
 5581, 
 5623, 
 5641, 
 5647, 
 5653, 
 5659, 
 5683, 
 5689, 
 5701, 
 5737, 
 5743, 
 5749, 
 5779, 
 5791, 
 5821, 
 5827, 
 5839, 
 5851, 
 5857, 
 5869, 
 5881, 
 5923, 
 5953, 
 6007, 
 6037, 
 6043, 
 6067, 
 6073, 
 6079, 
 6091, 
 6121, 
 6133, 
 6151, 
 6163, 
 6199, 
 6211, 
 6217, 
 6229, 
 6247, 
 6271, 
 6277, 
 6301, 
 6337, 
 6343, 
 6361, 
 6367, 
 6373, 
 6379, 
 6397, 
 6421, 
 6427, 
 6451, 
 6469, 
 6481, 
 6529, 
 6547, 
 6553, 
 6571, 
 6577, 
 6607, 
 6619, 
 6637, 
 6661, 
 6673, 
 6679, 
 6691, 
 6703, 
 6709, 
 6733, 
 6763, 
 6781, 
 6793, 
 6823, 
 6829, 
 6841, 
 6871, 
 6883, 
 6907, 
 6949, 
 6961, 
 6967, 
 6991, 
 6997, 
 7027, 
 7039, 
 7057, 
 7069, 
 7129, 
 7159, 
 7177, 
 7207, 
 7213, 
 7219, 
 7237, 
 7243, 
 7297, 
 7309, 
 7321, 
 7333, 
 7351, 
 7369, 
 7393, 
 7411, 
 7417, 
 7459, 
 7477, 
 7489, 
 7507, 
 7537, 
 7549, 
 7561, 
 7573, 
 7591, 
 7603, 
 7621, 
 7639, 
 7669, 
 7681, 
 7687, 
 7699, 
 7717, 
 7723, 
 7741, 
 7753, 
 7759, 
 7789, 
 7867, 
 7873, 
 7879, 
 7927, 
 7933, 
 7951, 
 7963, 
 7993, 
 8011, 
 8017, 
 8053, 
 8059, 
 8089, 
 8101, 
 8161, 
 8167, 
 8179, 
 8191, 
 8209, 
 8221, 
 8233, 
 8263, 
 8269, 
 8287, 
 8293, 
 8311, 
 8317, 
 8329, 
 8353, 
 8377, 
 8389, 
 8419, 
 8431, 
 8443, 
 8461, 
 8467, 
 8521, 
 8527, 
 8539, 
 8563, 
 8581, 
 8599, 
 8623, 
 8629, 
 8641, 
 8647, 
 8677, 
 8689, 
 8707, 
 8713, 
 8719, 
 8731, 
 8737, 
 8761, 
 8779, 
 8803, 
 8821, 
 8839, 
 8863, 
 8887, 
 8893, 
 8923, 
 8929, 
 8941, 
 8971, 
 9001, 
 9007, 
 9013, 
 9043, 
 9049, 
 9067, 
 9091, 
 9103, 
 9109, 
 9127, 
 9133, 
 9151, 
 9157, 
 9181, 
 9187, 
 9199, 
 9241, 
 9277, 
 9283, 
 9319, 
 9337, 
 9343, 
 9349, 
 9391, 
 9397, 
 9403, 
 9421, 
 9433, 
 9439, 
 9463, 
 9511, 
 9547, 
 9601, 
 9613, 
 9619, 
 9631, 
 9643, 
 9649, 
 9661, 
 9679, 
 9697, 
 9721, 
 9733, 
 9739, 
 9769, 
 9781, 
 9787, 
 9811, 
 9817, 
 9829, 
 9859, 
 9871, 
 9883, 
 9901, 
 9907, 
 9931, 
 9949, 
 9967, 
 9973, 
 10009, 
 10039, 
 10069, 
 10093, 
 10099, 
 10111, 
 10141, 
 10159, 
 10177, 
 10243, 
 10267, 
 10273, 
 10303, 
 10321, 
 10333, 
 10357, 
 10369, 
 10399, 
 10429, 
 10453, 
 10459, 
 10477, 
 10501, 
 10513, 
 10531, 
 10567, 
 10597, 
 10627, 
 10639, 
 10651, 
 10657, 
 10663, 
 10687, 
 10711, 
 10723, 
 10729, 
 10753, 
 10771, 
 10789, 
 10831, 
 10837, 
 10861, 
 10867, 
 10891, 
 10903, 
 10909, 
 10939, 
 10957, 
 10987, 
 10993, 
 11047, 
 11059, 
 11071, 
 11083, 
 11113, 
 11119, 
 11131, 
 11149, 
 11161, 
 11173, 
 11197, 
 11239, 
 11251, 
 11257, 
 11287, 
 11299, 
 11311, 
 11317, 
 11329, 
 11353, 
 11383, 
 11437, 
 11443, 
 11467, 
 11491, 
 11497, 
 11503, 
 11527, 
 11551, 
 11587, 
 11593, 
 11617, 
 11677, 
 11689, 
 11701, 
 11719, 
 11731, 
 11743, 
 11779, 
 11821, 
 11827, 
 11833, 
 11839, 
 11863, 
 11887, 
 11923, 
 11941, 
 11953, 
 11959, 
 11971, 
 12007, 
 12037, 
 12043, 
 12049, 
 12073, 
 12097, 
 12109, 
 12157, 
 12163, 
 12211, 
 12241, 
 12253, 
 12277, 
 12289, 
 12301, 
 12343, 
 12373, 
 12379, 
 12391, 
 12409, 
 12421, 
 12433, 
 12451, 
 12457, 
 12487, 
 12511, 
 12517, 
 12541, 
 12547, 
 12553, 
 12577, 
 12583, 
 12589, 
 12601, 
 12613, 
 12619, 
 12637, 
 12697, 
 12703, 
 12721, 
 12739, 
 12757, 
 12763, 
 12781, 
 12799, 
 12823, 
 12829, 
 12841, 
 12853, 
 12889, 
 12907, 
 12919, 
 12967, 
 12973, 
 12979, 
 13003, 
 13009, 
 13033, 
 13063, 
 13093, 
 13099, 
 13147, 
 13159, 
 13171, 
 13177, 
 13183, 
 13219, 
 13249, 
 13267, 
 13291, 
 13297, 
 13309, 
 13327, 
 13339, 
 13381, 
 13399, 
 13411, 
 13417, 
 13441, 
 13477, 
 13513, 
 13537, 
 13567, 
 13591, 
 13597, 
 13627, 
 13633, 
 13669, 
 13681, 
 13687, 
 13693, 
 13711, 
 13723, 
 13729, 
 13759, 
 13789, 
 13807, 
 13831, 
 13873, 
 13879, 
 13903, 
 13921, 
 13933, 
 13963, 
 13999, 
 14011, 
 14029, 
 14071, 
 14083, 
 14107, 
 14143, 
 14149, 
 14173, 
 14197, 
 14221, 
 14251, 
 14281, 
 14293, 
 14323, 
 14341, 
 14347, 
 14389, 
 14401, 
 14407, 
 14419, 
 14431, 
 14437, 
 14449, 
 14461, 
 14479, 
 14503, 
 14533, 
 14551, 
 14557, 
 14563, 
 14593, 
 14629, 
 14653, 
 14683, 
 14713, 
 14731, 
 14737, 
 14767, 
 14779, 
 14797, 
 14821, 
 14827, 
 14851, 
 14869, 
 14887, 
 14923, 
 14929, 
 14947, 
 14983, 
 15013, 
 15031, 
 15061, 
 15073, 
 15091, 
 15121, 
 15139, 
 15187, 
 15193, 
 15199, 
 15217, 
 15241, 
 15259, 
 15271, 
 15277, 
 15289, 
 15307, 
 15313, 
 15319, 
 15331, 
 15349, 
 15361, 
 15373, 
 15391, 
 15427, 
 15439, 
 15451, 
 15493, 
 15511, 
 15541, 
 15559, 
 15583, 
 15601, 
 15607, 
 15619, 
 15643, 
 15649, 
 15661, 
 15667, 
 15679, 
 15727, 
 15733, 
 15739, 
 15787, 
 15817, 
 15823, 
 15859, 
 15877, 
 15889, 
 15901, 
 15907, 
 15913, 
 15919, 
 15937, 
 15973, 
 15991, 
 16033, 
 16057, 
 16063, 
 16069, 
 16087, 
 16111, 
 16141, 
 16183, 
 16189, 
 16231, 
 16249, 
 16267, 
 16273, 
 16333, 
 16339, 
 16363, 
 16369, 
 16381, 
 16411, 
 16417, 
 16447, 
 16453, 
 16477, 
 16519, 
 16561, 
 16567, 
 16573, 
 16603, 
 16633, 
 16651, 
 16657, 
 16693, 
 16699, 
 16729, 
 16741, 
 16747, 
 16759, 
 16831, 
 16843, 
 16879, 
 16903, 
 16921, 
 16927, 
 16963, 
 16981, 
 16987, 
 16993, 
 17011, 
 17029, 
 17041, 
 17047, 
 17053, 
 17077, 
 17107, 
 17137, 
 17167, 
 17191, 
 17203, 
 17209, 
 17239, 
 17257, 
 17293, 
 17299, 
 17317, 
 17341, 
 17359, 
 17377, 
 17383, 
 17389, 
 17401, 
 17419, 
 17431, 
 17443, 
 17449, 
 17467, 
 17491, 
 17497, 
 17509, 
 17539, 
 17551, 
 17569, 
 17581, 
 17599, 
 17623, 
 17659, 
 17683, 
 17707, 
 17713, 
 17737, 
 17749, 
 17761, 
 17791, 
 17827, 
 17839, 
 17851, 
 17863, 
 17881, 
 17911, 
 17923, 
 17929, 
 17959, 
 17971, 
 17977, 
 17989, 
 18013, 
 18043, 
 18049, 
 18061, 
 18097, 
 18121, 
 18127, 
 18133, 
 18169, 
 18181, 
 18199, 
 18211, 
 18217, 
 18223, 
 18229, 
 18253, 
 18289, 
 18301, 
 18307, 
 18313, 
 18367, 
 18379, 
 18397, 
 18427, 
 18433, 
 18439, 
 18451, 
 18457, 
 18481, 
 18493, 
 18517, 
 18523, 
 18541, 
 18553, 
 18583, 
 18637, 
 18661, 
 18679, 
 18691, 
 18757, 
 18787, 
 18793, 
 18859, 
 18913, 
 18919, 
 18973, 
 18979, 
 19009, 
 19051, 
 19069, 
 19081, 
 19087, 
 19141, 
 19183, 
 19207, 
 19213, 
 19219, 
 19231, 
 19237, 
 19249, 
 19267, 
 19273, 
 19309, 
 19333, 
 19381, 
 19387, 
 19417, 
 19423, 
 19429, 
 19441, 
 19447, 
 19471, 
 19477, 
 19483, 
 19489, 
 19501, 
 19507, 
 19531, 
 19543, 
 19597, 
 19603, 
 19609, 
 19681, 
 19687, 
 19699, 
 19717, 
 19753, 
 19759, 
 19777, 
 19801, 
 19813, 
 19819, 
 19843, 
 19861, 
 19867, 
 19891, 
 19927, 
 19963, 
 19993, 
 20011, 
 20023, 
 20029, 
 20047, 
 20071, 
 20089, 
 20101, 
 20107, 
 20113, 
 20143, 
 20149, 
 20161, 
 20173, 
 20233, 
 20269, 
 20287, 
 20323, 
 20341, 
 20347, 
 20353, 
 20359, 
 20389, 
 20407, 
 20431, 
 20443, 
 20479, 
 20509, 
 20521, 
 20533, 
 20551, 
 20563, 
 20593, 
 20599, 
 20611, 
 20641, 
 20707, 
 20719, 
 20731, 
 20743, 
 20749, 
 20773, 
 20809, 
 20857, 
 20887, 
 20899, 
 20929, 
 20947, 
 20959, 
 20983, 
 21001, 
 21013, 
 21019, 
 21031, 
 21061, 
 21067, 
 21121, 
 21139, 
 21157, 
 21163, 
 21169, 
 21187, 
 21193, 
 21211, 
 21247, 
 21277, 
 21283, 
 21313, 
 21319, 
 21379, 
 21391, 
 21397, 
 21433, 
 21481, 
 21487, 
 21493, 
 21499, 
 21517, 
 21523, 
 21529, 
 21559, 
 21577, 
 21589, 
 21601, 
 21613, 
 21649, 
 21661, 
 21673, 
 21727, 
 21739, 
 21751, 
 21757, 
 21787, 
 21799, 
 21817, 
 21841, 
 21859, 
 21871, 
 21937, 
 21943, 
 21961, 
 21991, 
 21997, 
 22003, 
 22027, 
 22039, 
 22051, 
 22063, 
 22093, 
 22111, 
 22123, 
 22129, 
 22147, 
 22153, 
 22159, 
 22171, 
 22189, 
 22273, 
 22279, 
 22291, 
 22303, 
 22369, 
 22381, 
 22441, 
 22447, 
 22453, 
 22483, 
 22501, 
 22531, 
 22543, 
 22549, 
 22567, 
 22573, 
 22621, 
 22639, 
 22651, 
 22669, 
 22699, 
 22717, 
 22741, 
 22777, 
 22783, 
 22807, 
 22861, 
 22921, 
 22963, 
 22993, 
 23011, 
 23017, 
 23029, 
 23041, 
 23053, 
 23059, 
 23071, 
 23131, 
 23143, 
 23167, 
 23173, 
 23197, 
 23203, 
 23209, 
 23227, 
 23251, 
 23269, 
 23293, 
 23311, 
 23371, 
 23431, 
 23473, 
 23497, 
 23509, 
 23539, 
 23557, 
 23563, 
 23581, 
 23593, 
 23599, 
 23623, 
 23629, 
 23671, 
 23677, 
 23689, 
 23719, 
 23743, 
 23761, 
 23767, 
 23773, 
 23827, 
 23833, 
 23857, 
 23869, 
 23887, 
 23893, 
 23899, 
 23911, 
 23917, 
 23929, 
 23971, 
 23977, 
 24001, 
 24007, 
 24019, 
 24043, 
 24049, 
 24061, 
 24091, 
 24097, 
 24103, 
 24109, 
 24121, 
 24133, 
 24151, 
 24169, 
 24181, 
 24223, 
 24229, 
 24247, 
 24337, 
 24373, 
 24379, 
 24391, 
 24421, 
 24439, 
 24469, 
 24481, 
 24499, 
 24517, 
 24547, 
 24571, 
 24631, 
 24691, 
 24697, 
 24709, 
 24733, 
 24763, 
 24781, 
 24793, 
 24799, 
 24841, 
 24847, 
 24859, 
 24877, 
 24889, 
 24907, 
 24919, 
 24943, 
 24967, 
 24979, 
 25033, 
 25057, 
 25087, 
 25111, 
 25117, 
 25147, 
 25153, 
 25171, 
 25183, 
 25189, 
 25219, 
 25237, 
 25243, 
 25261, 
 25303, 
 25309, 
 25321, 
 25339, 
 25357, 
 25411, 
 25423, 
 25447, 
 25453, 
 25471, 
 25537, 
 25561, 
 25579, 
 25603, 
 25609, 
 25621, 
 25633, 
 25639, 
 25657, 
 25693, 
 25717, 
 25741, 
 25747, 
 25759, 
 25771, 
 25801, 
 25819, 
 25849, 
 25867, 
 25873, 
 25903, 
 25933, 
 25939, 
 25951, 
 25969, 
 25981, 
 25999, 
 26017, 
 26029, 
 26041, 
 26053, 
 26083, 
 26107, 
 26113, 
 26119, 
 26161, 
 26203, 
 26209, 
 26227, 
 26251, 
 26263, 
 26293, 
 26317, 
 26347, 
 26371, 
 26407, 
 26431, 
 26437, 
 26449, 
 26479, 
 26497, 
 26539, 
 26557, 
 26641, 
 26647, 
 26683, 
 26701, 
 26713, 
 26731, 
 26737, 
 26821, 
 26833, 
 26839, 
 26863, 
 26881, 
 26893, 
 26947, 
 26953, 
 26959, 
 27031, 
 27043, 
 27061, 
 27067, 
 27073, 
 27091, 
 27103, 
 27109, 
 27127, 
 27211, 
 27241, 
 27253, 
 27259, 
 27271, 
 27277, 
 27283, 
 27337, 
 27361, 
 27367, 
 27397, 
 27409, 
 27427, 
 27457, 
 27481, 
 27487, 
 27529, 
 27541, 
 27583, 
 27631, 
 27673, 
 27691, 
 27697, 
 27733, 
 27739, 
 27751, 
 27763, 
 27793, 
 27799, 
 27817, 
 27823, 
 27847, 
 27883, 
 27901, 
 27919, 
 27943, 
 27961, 
 27967, 
 27997, 
 28027, 
 28051, 
 28057, 
 28069, 
 28081, 
 28087, 
 28099, 
 28111, 
 28123, 
 28183, 
 28201, 
 28219, 
 28279, 
 28297, 
 28309, 
 28351, 
 28387, 
 28393, 
 28411, 
 28429, 
 28447, 
 28477, 
 28513, 
 28537, 
 28549, 
 28573, 
 28579, 
 28591, 
 28597, 
 28603, 
 28621, 
 28627, 
 28657, 
 28663, 
 28669, 
 28687, 
 28711, 
 28723, 
 28729, 
 28753, 
 28759, 
 28771, 
 28789, 
 28807, 
 28813, 
 28837, 
 28843, 
 28867, 
 28879, 
 28909, 
 28921, 
 28927, 
 28933, 
 29017, 
 29023, 
 29059, 
 29077, 
 29101, 
 29131, 
 29137, 
 29167, 
 29173, 
 29179, 
 29191, 
 29209, 
 29221, 
 29251, 
 29269, 
 29287, 
 29311, 
 29347, 
 29383, 
 29389, 
 29401, 
 29437, 
 29443, 
 29473, 
 29527, 
 29569, 
 29581, 
 29587, 
 29599, 
 29611, 
 29629, 
 29641, 
 29671, 
 29683, 
 29761, 
 29803, 
 29833, 
 29851, 
 29863, 
 29881, 
 29917, 
 29947, 
 29959, 
 29983, 
 29989, 
 30013, 
 30091, 
 30097, 
 30103, 
 30109, 
 30133, 
 30139, 
 30169, 
 30181, 
 30187, 
 30211, 
 30223, 
 30241, 
 30253, 
 30259, 
 30271, 
 30307, 
 30313, 
 30319, 
 30367, 
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