gap> Factors(1093^28+1:Pminus1Limit1:=250000,ECMCurves:=256,ECMLimit1:=10000, ECMDelta:=100,ECMLimit2:=1000000,Pplus1Limit1:=25000); #I #I Check for n = b^k +/- 1 #I 120604783831868319714361188926040065699900262125810019185409703521265062910696\ 10672402 = 1093^28 + 1 #I The factors corresponding to polynomial factors are [ 1427186233202, 8450528811596114346412493592648523582188327098989722278623638076982859601 ] #I #I Factors already found : [ ] #I #I #I Trial division by all primes p < 1000 #I Intermediate result : [ [ 2, 41, 17404710161 ], [ ] ] #I #I Factors already found : [ 2, 41, 17404710161 ] #I #I #I Trial division by some already known primes #I #I Check for perfect powers #I #I Pollard's Rho Steps = 16384, Cluster = 795 Number to be factored : 8450528811596114346412493592648523582188327098989722278623638076982859601 #I Intermediate result : [ [ 68489 ], [ 123385197792289482200243741223386581526790099125256935838216911\ 868809 ] ] #I #I Factors already found : [ 2, 41, 68489, 17404710161 ] #I #I #I Pollard's p - 1 Limit1 = 250000, Limit2 = 10000000 Number to be factored : 123385197792289482200243741223386581526790099125256935838216911868809 #I Initializing prime differences list, PrimeDiffLimit = 10000000 #I p-1 for n = 123385197792289482200243741223386581526790099125256935838216911868809 a : 2, Limit1 : 250000, Limit2 : 10000000 #I First stage #I Second stage #I #I Williams' p + 1 Residues = 2, Limit1 = 25000, Limit2 = 1000000 Number to be factored : 123385197792289482200243741223386581526790099125256935838216911868809 #I p+1 for n = 123385197792289482200243741223386581526790099125256935838216911868809 Residues : 2, Limit1 : 25000, Limit2 : 1000000 #I Residue no. 1 #I First stage #I Second stage #I Residue no. 2 #I First stage #I Second stage #I #I Elliptic Curves Method (ECM) Curves = 256 Init. Limit1 = 10000, Init. Limit2 = 1000000, Delta = 100 Number to be factored : 123385197792289482200243741223386581526790099125256935838216911868809 #I ECM for n = 123385197792289482200243741223386581526790099125256935838216911868809 Curves : 256, Initial Limit1 : 10000, Initial Limit2 : 1000000, Delta : 100 #I Curve no. 1, Limit1 : 10000, Limit2 : 1000000 #I First stage #I Second stage #I Curve no. 2, Limit1 : 10100, Limit2 : 1010000 #I First stage #I Second stage #I Curve no. 3, Limit1 : 10200, Limit2 : 1020000 #I First stage #I Second stage #I Curve no. 4, Limit1 : 10300, Limit2 : 1030000 #I First stage #I Second stage #I Curve no. 5, Limit1 : 10400, Limit2 : 1040000 #I First stage #I Second stage #I Curve no. 6, Limit1 : 10500, Limit2 : 1050000 #I First stage #I Second stage #I Curve no. 7, Limit1 : 10600, Limit2 : 1060000 #I First stage #I Second stage #I Curve no. 8, Limit1 : 10700, Limit2 : 1070000 #I First stage #I Second stage #I Curve no. 9, Limit1 : 10800, Limit2 : 1080000 #I First stage #I Second stage #I Curve no. 10, Limit1 : 10900, Limit2 : 1090000 #I First stage #I Second stage #I Curve no. 11, Limit1 : 11000, Limit2 : 1100000 #I First stage #I Second stage #I Curve no. 12, Limit1 : 11100, Limit2 : 1110000 #I First stage #I Second stage #I Curve no. 13, Limit1 : 11200, Limit2 : 1120000 #I First stage #I Second stage #I Curve no. 14, Limit1 : 11300, Limit2 : 1130000 #I First stage #I Second stage #I Curve no. 15, Limit1 : 11400, Limit2 : 1140000 #I First stage #I Second stage #I Curve no. 16, Limit1 : 11500, Limit2 : 1150000 #I First stage #I Second stage #I Curve no. 17, Limit1 : 11600, Limit2 : 1160000 #I First stage #I Second stage #I Curve no. 18, Limit1 : 11700, Limit2 : 1170000 #I First stage #I Second stage #I Curve no. 19, Limit1 : 11800, Limit2 : 1180000 #I First stage #I Second stage #I Curve no. 20, Limit1 : 11900, Limit2 : 1190000 #I First stage #I Second stage #I Curve no. 21, Limit1 : 12000, Limit2 : 1200000 #I First stage #I Second stage #I Curve no. 22, Limit1 : 12100, Limit2 : 1210000 #I First stage #I Second stage #I Curve no. 23, Limit1 : 12200, Limit2 : 1220000 #I First stage #I Second stage #I Curve no. 24, Limit1 : 12300, Limit2 : 1230000 #I First stage #I Second stage #I Curve no. 25, Limit1 : 12400, Limit2 : 1240000 #I First stage #I Second stage #I Curve no. 26, Limit1 : 12500, Limit2 : 1250000 #I First stage #I Second stage #I Curve no. 27, Limit1 : 12600, Limit2 : 1260000 #I First stage #I Second stage #I Curve no. 28, Limit1 : 12700, Limit2 : 1270000 #I First stage #I Second stage #I Curve no. 29, Limit1 : 12800, Limit2 : 1280000 #I First stage #I Second stage #I Curve no. 30, Limit1 : 12900, Limit2 : 1290000 #I First stage #I Second stage #I Curve no. 31, Limit1 : 13000, Limit2 : 1300000 #I First stage #I Second stage #I Curve no. 32, Limit1 : 13100, Limit2 : 1310000 #I First stage #I Second stage #I Curve no. 33, Limit1 : 13200, Limit2 : 1320000 #I First stage #I Second stage #I Curve no. 34, Limit1 : 13300, Limit2 : 1330000 #I First stage #I Second stage #I Curve no. 35, Limit1 : 13400, Limit2 : 1340000 #I First stage #I Second stage #I Curve no. 36, Limit1 : 13500, Limit2 : 1350000 #I First stage #I Second stage #I Curve no. 37, Limit1 : 13600, Limit2 : 1360000 #I First stage #I Second stage #I Curve no. 38, Limit1 : 13700, Limit2 : 1370000 #I First stage #I Second stage #I Curve no. 39, Limit1 : 13800, Limit2 : 1380000 #I First stage #I Second stage #I Curve no. 40, Limit1 : 13900, Limit2 : 1390000 #I First stage #I Second stage #I Curve no. 41, Limit1 : 14000, Limit2 : 1400000 #I First stage #I Second stage #I Curve no. 42, Limit1 : 14100, Limit2 : 1410000 #I First stage #I Second stage #I Curve no. 43, Limit1 : 14200, Limit2 : 1420000 #I First stage #I Second stage #I Curve no. 44, Limit1 : 14300, Limit2 : 1430000 #I First stage #I Second stage #I Curve no. 45, Limit1 : 14400, Limit2 : 1440000 #I First stage #I Second stage #I Curve no. 46, Limit1 : 14500, Limit2 : 1450000 #I First stage #I Second stage #I Curve no. 47, Limit1 : 14600, Limit2 : 1460000 #I First stage #I Second stage #I Curve no. 48, Limit1 : 14700, Limit2 : 1470000 #I First stage #I Second stage #I Curve no. 49, Limit1 : 14800, Limit2 : 1480000 #I First stage #I Second stage #I Curve no. 50, Limit1 : 14900, Limit2 : 1490000 #I First stage #I Second stage #I Curve no. 51, Limit1 : 15000, Limit2 : 1500000 #I First stage #I Second stage #I Curve no. 52, Limit1 : 15100, Limit2 : 1510000 #I First stage #I Second stage #I Curve no. 53, Limit1 : 15200, Limit2 : 1520000 #I First stage #I Second stage #I Curve no. 54, Limit1 : 15300, Limit2 : 1530000 #I First stage #I Second stage #I Curve no. 55, Limit1 : 15400, Limit2 : 1540000 #I First stage #I Second stage #I Curve no. 56, Limit1 : 15500, Limit2 : 1550000 #I First stage #I Second stage #I Curve no. 57, Limit1 : 15600, Limit2 : 1560000 #I First stage #I Second stage #I Curve no. 58, Limit1 : 15700, Limit2 : 1570000 #I First stage #I Second stage #I Curve no. 59, Limit1 : 15800, Limit2 : 1580000 #I First stage #I Second stage #I Curve no. 60, Limit1 : 15900, Limit2 : 1590000 #I First stage #I Second stage #I Curve no. 61, Limit1 : 16000, Limit2 : 1600000 #I First stage #I Second stage #I Curve no. 62, Limit1 : 16100, Limit2 : 1610000 #I First stage #I Second stage #I Curve no. 63, Limit1 : 16200, Limit2 : 1620000 #I First stage #I Second stage #I Curve no. 64, Limit1 : 16300, Limit2 : 1630000 #I First stage #I Second stage #I Curve no. 65, Limit1 : 16400, Limit2 : 1640000 #I First stage #I Second stage #I Curve no. 66, Limit1 : 16500, Limit2 : 1650000 #I First stage #I Second stage #I Curve no. 67, Limit1 : 16600, Limit2 : 1660000 #I First stage #I Second stage #I Curve no. 68, Limit1 : 16700, Limit2 : 1670000 #I First stage #I Second stage #I Curve no. 69, Limit1 : 16800, Limit2 : 1680000 #I First stage #I Second stage #I Curve no. 70, Limit1 : 16900, Limit2 : 1690000 #I First stage #I Second stage #I Curve no. 71, Limit1 : 17000, Limit2 : 1700000 #I First stage #I Second stage #I Curve no. 72, Limit1 : 17100, Limit2 : 1710000 #I First stage #I Second stage #I Curve no. 73, Limit1 : 17200, Limit2 : 1720000 #I First stage #I Second stage #I Curve no. 74, Limit1 : 17300, Limit2 : 1730000 #I First stage #I Second stage #I Curve no. 75, Limit1 : 17400, Limit2 : 1740000 #I First stage #I Second stage #I Curve no. 76, Limit1 : 17500, Limit2 : 1750000 #I First stage #I Second stage #I Factor 424747962122189061704041 was found #I Intermediate result : [ [ 424747962122189061704041, 290490382051073231478800385526362271396418849 ], [ ] ] #I #I The result is [ [ 2, 41, 68489, 17404710161, 424747962122189061704041, 290490382051073231478800385526362271396418849 ], [ ] ] [ 2, 41, 68489, 17404710161, 424747962122189061704041, 290490382051073231478800385526362271396418849 ] gap>