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  1. from math import *
  2. from random import *
  3.  
  4. primes = [2, 3, 5, 7, 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]
  5.  
  6.  
  7.  
  8. count = 0
  9. icount = 0 #iterp iterations performed (all loops)
  10. fcount = 0 #factorizations performed
  11. ncount = 0 #nextp iterations performed
  12.  
  13.  
  14. def genNm0(p):
  15. i = 0
  16. while primes[i]**2 < p**0.5:
  17. i = i + 1
  18.  
  19. #now back off to get the final value
  20. if i > 0:
  21. #the check makes sure we dont fall off the left side of the prime number line
  22. i = i - 1
  23.  
  24. series = []
  25. #calculate the initial entry in the series
  26. i = primes[i]
  27. series.append([2, i, 2**i])
  28. i = i - 1
  29. #now calculate the rest of the series
  30. while i > 1:
  31. series.append([2, i, 2**i])
  32. i = i - 1
  33. return series
  34.  
  35. #groups are like so I**Nm,
  36. #consume a series, and rewrite its terms
  37. def genNm1(series, circuit=[2, 3, 5, 7]):
  38. s = series.reverse()
  39. i = 0
  40. I = 0
  41. circuit = circuit
  42. n = min(circuit)
  43. while i < len(series):
  44. #series[i][1] = circuit[n]
  45. #n = n+1
  46. #if n >= len(circuit):
  47. # n = 0
  48.  
  49. series[i][1] = n
  50. n = n + 1
  51. if n > max(circuit):
  52. n = min(circuit)
  53. i = i + 1
  54.  
  55. #we can return the series here, or we can go head and update the I values as well.
  56. #probably keep it simple just to do it the current way
  57. return series
  58.  
  59.  
  60. def genI(series, circuit=[2, 3, 5, 7]):
  61. circuit = circuit
  62. n = 0
  63. i = 0
  64. while i < len(series):
  65. series[i][0] = circuit[n]
  66. n = n + 1
  67. if n >= len(circuit):
  68. n = 0
  69. i = i + 1
  70.  
  71. return series
  72.  
  73.  
  74.  
  75. #subtracts the series from p
  76. def subSeries(p, series):
  77. i = 0
  78. series = series
  79. series.reverse()
  80. result = p
  81. while i < len(series):
  82. result = abs(result - ((series[i][0])**(series[i][1])))
  83. i = i + 1
  84.  
  85. return result
  86.  
  87. def plusSeries(p, series):
  88. i = 0
  89. series = series
  90. series.reverse()
  91. result = 0
  92. while i < len(series):
  93. result = result + ((series[i][0])**(series[i][1]))
  94. i = i + 1
  95.  
  96. return result
  97.  
  98.  
  99. #try subSeries(p, genI(genNm1(genNm0(p))))
  100.  
  101. def factor(p, mf=32):
  102. factors = []
  103. i = 0
  104. #global count
  105. global fcount
  106. while i < mf:
  107. if p%primes[i] == 0:
  108. factors.append(primes[i])
  109. p = p / primes[i]
  110. #count = count + 1
  111. fcount = fcount +1
  112. else:
  113. i = i + 1
  114. #count = count + 1
  115. fcount = fcount+1
  116. #this way we catch ALL instances of say 2, 3, etc. Basically all exponents, so 12 for example is 12/2/2 = 3, or 2**2*3
  117.  
  118. return factors
  119.  
  120.  
  121. #the total product of all numbers within the list
  122. def lsp(ls):
  123. i = 0
  124. result = 1
  125. while i < len(ls):
  126. result = result*ls[i]
  127.  
  128. return result
  129.  
  130.  
  131. #returns the list of all partial products, as they are calculated at each step, instead of a single total product from lsp
  132. def nextp(ls):
  133. i = 0
  134. results = []
  135. result = 1
  136. #global count
  137. global ncount
  138. while i < len(ls):
  139. #count = count + 1
  140. ncount = ncount+1
  141. result = result*ls[i]
  142. results.append(result)
  143. i = i + 1
  144.  
  145. return results
  146.  
  147.  
  148.  
  149. #some 'circuits' of starting value I experimented with
  150. circuit1 =[-3, -5, -9, 11, 23, 47, 95, 191, 383, 767] #this generates spline sets that are powers of 2, for some reason
  151. circuit2 = [3, 5, 9, 11, 23, 47, 95, 191, 383, 767]
  152. circuit3 = [3, 5, 9, -11, -23, -47, -95, -191, -383, -767]
  153. circuit1b = [767, 383, 191, 95, 47, 23, 11, -9, -5, -3]
  154. circuit2b = [767, 383, 191, 95, 47, 23, 11, 9, 5, 3]
  155. circuit1c = [-3, -5, 11, 23, 47, 95, 191, 383, 767]
  156.  
  157. #iterate potential products congruent to a-k || b-k
  158. #p [int]: your product. you can use randp() to get a random one if you dont have a number on hand. already done for you at the bottom
  159. #of the script, so you can try experimenting.
  160. #i [int]: starting estimate of i. can be i=[int], i='mx' to set it to the value of mx*-1, or i='log' to let the code attempt an estimate
  161. #mx [int]: is the max iterations of the outer loop
  162. #km [int]: is the max iterations of the innerloop k
  163. #invertI [bool]: debug argument for experimentation
  164. #circuit [list]: what exponents to use initially when generating the series.
  165. #mf [int]: the number of factors to check during factoring, options - mf= [int], mf='log': estimates it for you
  166. def iterp(p, i=None, mx=10, km=1, invertI=True, circuit=[2, 3, 5, 7], mf='log'):
  167. #global count
  168. global icount
  169. global fcount
  170. global ncount
  171. count = 0
  172. circuit = circuit
  173. val = plusSeries(p, genI(genNm1(genNm0(p), circuit), circuit)) #instead of subSeries
  174. mx = mx
  175. if mf=='log':
  176. mf = ceil(log(p))
  177. if i == None:
  178. i = mx*-1
  179. elif i=='log':
  180. i = (floor(log(p**2))-1)
  181. elif i=='mx':
  182. i = mx*-1
  183. else:
  184. i = i
  185. mx = mx+i
  186. if invertI==True and i!=None and i!='log':
  187. i = i*-1
  188.  
  189. k = km*-1
  190. mx = (abs(mx)+i)
  191. print(f"val: {val}, i: {i}, mx: {mx}")
  192. while i <= mx:
  193. print(f"i: {i}")
  194. f = factor(abs(p-val--i), mf) #--i so we don't have to perform a check when i goes negative, it'll just start adding instead of minus
  195. print(f"f: {f}")
  196. spline = nextp(f) #now we need to calculate our potential factors from here
  197. print(f"spline: {spline}")
  198. j = 0
  199. while j < len(spline):
  200. k = km*-1
  201. while k <= km:
  202. icount = icount + 1
  203. if ((spline[j])-k) > 0:
  204. if p%((spline[j])-k) == 0 and ((spline[j])-k) > 1:
  205. print(f"fcount: {fcount}, icount: {icount}, ncount: {ncount}, total: {fcount+icount+ncount}, found factors! mod: {k}, i: {i}, j: {j}, k: {k}, factor: {((spline[j])-k)}, factor: {p/((spline[j])-k)}")
  206. fcount, icount, ncount = 0, 0, 0
  207. return ((spline[j])-k), p/((spline[j])-k), True
  208. #else
  209. k = k + 1
  210. j = j + 1
  211.  
  212. i = i + 1
  213.  
  214. #else
  215. print("no factors found!")
  216. #reset global counts. Used globals so I wouldn't havent to instrument all functions with arguments and extra returns for accumulators
  217. fcount, icount, ncount = 0, 0, 0
  218. #last return 'False' is for debugging.
  219. #return factor A, factor B, [bool] to keep track of number of successes, in simple terms
  220. return None, None, False
  221.  
  222. #m is a small number to skip over trivial primes during generation
  223. def randp(m=10):
  224. x = primes[randint(m, len(primes)-1)]
  225. y = primes[randint(m, len(primes)-1)]
  226. if x < y:
  227. a = x
  228. b = y
  229. else:
  230. b = x
  231. a = y
  232.  
  233. return a*b, a, b
  234.  
  235. def test(circuit=[2,3,5,7], n=None):
  236. p, a, b = randp()
  237. if n == None:
  238. n = floor(p**0.5)
  239.  
  240. result = None
  241. i = 0
  242. while i < n:
  243. result = iterp(p, 'log', 8, i, False, circuit1, 1)
  244. if result[2] == True:
  245. return None #all done
  246. #else
  247. print("no factor found.")
  248. return None
  249.  
  250.  
  251. print("try typing 'test()' to get started with a product and two factors.")
  252.  
  253. print("then try 'iterp(p, 'log', 8, i, False, circuit1, 1)'")
  254.  
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