(17*10^31-71)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(17*10^31-71)/99 N=1717171717171717171717171717171 Factor: 2 divides N - 1 Factor: 2^2 divides N + 1 Factor: 3 divides N - 1 Factor: 5 divides N - 1 Factor: 7 divides N - 1 Factor: 11 divides N + 1 Factor: 13 divides N - 1 Factor: 17 divides N - 1 Factor: 23 divides N + 1 Factor: 31 divides N - 1 Factor: 37 divides N - 1 Factor: 41 divides N - 1 Factorization results: F1=0.3089 F2=0.0994 F1=2182523070 F2=1012 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=71717171717171717169 Pass: 3^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=29 p=1 q=-7 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=29 p=3 q=-5 R20=74368468112633149632 Pass: U{N+1} = 0 (mod N): d=29 p=3 q=-5 R20=0 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=24873081318416479731 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=36145982538848188424 Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=34733506295431959533 Pass: gcd(U{(N+1)/11}, N) = 1: d=29 p=3 q=-5 R20=75889137708777222826 Fail: gcd(3^((N-1)/13) - 1, N) not = 1: R20=0 Pass: gcd(7^((N-1)/13) - 1, N) = 1: R20=82754993074923534708 Pass: 7^(N-1) = 1 (mod N): R20=1 Pass: gcd(7^((N-1)/17) - 1, N) = 1: R20=56145531162052704949 Pass: gcd(U{(N+1)/23}, N) = 1: d=29 p=3 q=-5 R20=9893756714395431819 Pass: gcd(7^((N-1)/31) - 1, N) = 1: R20=89358476954355236642 Pass: gcd(7^((N-1)/37) - 1, N) = 1: R20=29054232281828764225 Pass: gcd(7^((N-1)/41) - 1, N) = 1: R20=6531438961362544188 BLS tests passed: F1=0.3089 F2=0.0994 Main divisor test: F1=0.2989 F2=0.0994 G=0.3983 S=0.0000 T=1 G=1104356673420 Main divisor test passed: 1/1 Final divisor test: F=0.3089 G=0.3983 H=1.0161 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec
(17*10^37-71)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(17*10^37-71)/99 N=1717171717171717171717171717171717171 Factor: 2 divides N - 1 Factor: 2^2 divides N + 1 Factor: 3^2 divides N - 1 Factor: 5 divides N - 1 Factor: 7 divides N - 1 Factor: 13 divides N - 1 Factor: 17 divides N - 1 Factor: 19 divides N - 1 Factor: 37 divides N - 1 Factor: 101 divides N - 1 Factor: 9901 divides N - 1 Factorization results: F1=0.3861 F2=0.0166 F1=97878787878690 F2=4 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=71717171717171717169 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=48601905774926808122 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=35763837691649457780 Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=98408220656761682163 Pass: gcd(3^((N-1)/13) - 1, N) = 1: R20=41466020188593064714 Fail: gcd(3^((N-1)/17) - 1, N) not = 1: R20=0 Pass: gcd(7^((N-1)/17) - 1, N) = 1: R20=7153162019986157859 Pass: 7^(N-1) = 1 (mod N): R20=1 Pass: gcd(7^((N-1)/19) - 1, N) = 1: R20=82239478772342386392 Pass: gcd(7^((N-1)/37) - 1, N) = 1: R20=10975655667755510326 Pass: gcd(7^((N-1)/101) - 1, N) = 1: R20=64639804137182958668 Pass: gcd(7^((N-1)/9901) - 1, N) = 1: R20=74570143588062121701 BLS tests passed: F1=0.3861 F2=0.0166 Main divisor test: F1=0.3778 F2=0.0166 G=0.3944 S=0.0000 T=1 G=195757575757380 Main divisor test passed: 1/1 Final divisor test: F=0.3861 G=0.3944 H=1.1666 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec
(17*10^4885-71)/99 == ID:B27B6046426BC ============================================= PRIMO 1.2.2 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 171717171717171717171717171717171717171717171717171717171717\ ... ... [= 1(71)_2442 = (17*10^4885-71)/99] Decimal size = 4885 Binary size = 16226 ----------------------------------------------------------------- 1) EC Test ----------------------------------------------------------------- N = Candidate S = 266269524 R = 644899833588059132038397198310880358849168077219275448029558\ ... ... ... ----------------------------------------------------------------- 761) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 07.31.2002 08:27:52 PM Running time 2008h 56mn 53s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.2' by Hans Rosenthal. The proof was done using Marcel Martin's Primo and took 2008 hours and 57 minutes on a AMD Athlon 1.33 GHz. The Primo certificate was then validated with Cert_Val which took on the same PC an additional 25 hours and 11 minutes. The Primo certificate of the above record SUPP (the zipped file of which is > 2.5 MB) is available on demand by simple email request to Hans. Here are the first and last lines from the Cert_Val output file: +------------------------------------------------------------------------+ | Cert_Val a "PRIMO/Titanix" certificate (.out file) validation program | | Version 1.95 Jim Fougeron, Using the Miracl big integer library | | Copyright, 2001-2002 Jim Fougeron, Free usage rights granted to all | +------------------------------------------------------------------------+ Processing file primo-b27b6046426bc.out This Certificate is a PRIMO compatible certificate 1) EC Test ECtest1 != Ident, ECtest2= Ident Validated 8mn 1.379s 2) EC Test ECtest1 != Ident, ECtest2= Ident Validated 7mn 57.941s ... ... 761) SPP Test Trial-div to 170101 !Success!!! Validated 0.001s Prime number being certified was: N = 17171717171717171717171717171717171717171717171717\ ... 17171717171717171717171717171717171 Certificate for this number was FULLY validated! Total time used to validate certificate: 1 days 1h 10mn 59.059s There were 761 steps in the primality proof