*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(15*10^3-51)/99 N=151 *** N is prime! Time: 0 sec
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(15*10^15-51)/99 N=151515151515151 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3 divides N - 1 Factor: 5^2 divides N - 1 Factor: 239 divides N - 1 Factorization results: F1=0.3212 F2=0.0849 F1=35850 F2=16 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=151515151515149 Pass: 3^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=3 q=-1 R20=113543879236388 Pass: U{N+1} = 0 (mod N): d=13 p=3 q=-1 R20=0 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=134652178724280 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=56852794520023 Pass: gcd(3^((N-1)/239) - 1, N) = 1: R20=23337384295483 BLS tests passed: F1=0.3212 F2=0.0849 Main divisor test: F1=0.3000 F2=0.0849 G=0.3849 S=0.0000 T=1 G=286800 Main divisor test passed: 1/1 Final divisor test: F=0.3212 G=0.3849 H=1.0272 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(15*10^63-51)/99 N=151515151515151515151515151515151515151515151515151515151515151 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3 divides N - 1 Factor: 5^2 divides N - 1 Factor: 281 divides N + 1 Factor: 2791 divides N - 1 Factorization results: F1=0.0904 F2=0.0587 F1=418650 F2=4496 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=51515151515151515149 Pass: 3^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=3 q=-1 R20=60674099198985677568 Pass: U{N+1} = 0 (mod N): d=13 p=3 q=-1 R20=0 Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0 Fail: gcd(7^((N-1)/3) - 1, N) not = 1: R20=0 Pass: gcd(11^((N-1)/3) - 1, N) = 1: R20=80535677442945378449 Pass: 11^(N-1) = 1 (mod N): R20=1 Pass: gcd(11^((N-1)/5) - 1, N) = 1: R20=95303056095581401194 Pass: gcd(U{(N+1)/281}, N) = 1: d=13 p=3 q=-1 R20=93429673111965985462 Pass: gcd(11^((N-1)/2791) - 1, N) = 1: R20=77396757731622212701 BLS tests passed: F1=0.0904 F2=0.0587 APRCL test T=1260 S=1684033088848101075163079 APRCL main test (1) at level 4 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=51515151515151515150 APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=2 R20=15151515151515151515 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=51515151515151515150 APRCL L_2 condition satisfied APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=22036937421552806168 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=51515151515151515150 APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=0 R20=1 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=1 R20=40301971610759570985 APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=0 R20=1 APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=55189587622020054452 APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=3 R20=7940335561592543980 APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=65978452779879652650 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=0 R20=1 APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=51515151515151515150 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=51515151515151515150 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=51515151515151515150 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=0 R20=41300331871362276291 APRCL tests for p=2 completed APRCL main test (2) at level 4 for p=3 APRCL L_3 condition satisfied APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=1 R20=1 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=0 R20=2 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=51515151515151515148 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=6 R20=27216063329308824837 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=8 R20=27992687102478122925 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=7 R20=95244786275875588262 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=0 R20=2 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=8 R20=71029041505100243562 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=0 R20=2 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=0 R20=2 APRCL tests for p=3 completed APRCL main test (3) at level 4 for p=5 APRCL L_5 condition satisfied APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=4 R20=51515151515151515144 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=2 R20=1 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=4 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=4 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=3 R20=1 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=3 R20=1 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=1 APRCL tests for p=5 completed APRCL main test (4) at level 4 for p=7 APRCL L_7 condition satisfied APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=0 R20=68663017505684398340 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=1 R20=16277302001950567782 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=3 R20=90489449614072509426 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=5 R20=66058046285740032338 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=3 R20=1597365311294658426 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=5 R20=35249465512549722402 APRCL tests for p=7 completed Main divisor test: F1=0.0856 F2=0.0587 G=0.5339 S=0.3896 T=1260 G=1584885977548786893983067756490800 Main divisor test passed: 1260/1260 *** N is prime! Time: 1 sec |
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(15*10^89-51)/99 N=15151515151515151515151515151515151515151515151515151515151515151515151515151515151515151 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3 divides N - 1 Factor: 5^2 divides N - 1 Factor: 11 divides N - 1 Factor: 17 divides N + 1 Factor: 23 divides N - 1 Factor: 73 divides N - 1 Factor: 89 divides N - 1 Factor: 101 divides N - 1 Factor: 131 divides N + 1 Factor: 137 divides N - 1 Factor: 617 divides N - 1 Factor: 1427 divides N + 1 Factor: 4093 divides N - 1 Factor: 8779 divides N - 1 Factor: 21649 divides N - 1 Factorization results: F1=0.3086 F2=0.0874 F1=1637481439564425268940935050 F2=50846864 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=51515151515151515149 Pass: 3^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=3 q=-1 R20=149444611681840116 Pass: U{N+1} = 0 (mod N): d=13 p=3 q=-1 R20=0 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=28233816581556132674 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=43536317352282838500 Pass: gcd(3^((N-1)/11) - 1, N) = 1: R20=32885207827798692710 Pass: gcd(U{(N+1)/17}, N) = 1: d=13 p=3 q=-1 R20=24922046136978312371 Pass: gcd(3^((N-1)/23) - 1, N) = 1: R20=72566050431467841948 Fail: gcd(3^((N-1)/73) - 1, N) not = 1: R20=0 Pass: gcd(11^((N-1)/73) - 1, N) = 1: R20=90614276252907501512 Pass: 11^(N-1) = 1 (mod N): R20=1 Pass: gcd(11^((N-1)/89) - 1, N) = 1: R20=60977794470288353203 Pass: gcd(11^((N-1)/101) - 1, N) = 1: R20=92455738577165547277 Pass: gcd(U{(N+1)/131}, N) = 1: d=13 p=3 q=-1 R20=9203486369382552244 Pass: gcd(11^((N-1)/137) - 1, N) = 1: R20=29497027629353488569 Pass: gcd(11^((N-1)/617) - 1, N) = 1: R20=20842720093382346439 Pass: gcd(U{(N+1)/1427}, N) = 1: d=13 p=3 q=-1 R20=29304676142695025933 Pass: gcd(11^((N-1)/4093) - 1, N) = 1: R20=22614437604574288457 Pass: gcd(11^((N-1)/8779) - 1, N) = 1: R20=66923386650857514796 Pass: gcd(11^((N-1)/21649) - 1, N) = 1: R20=75598217672172859514 BLS tests passed: F1=0.3086 F2=0.0874 Main divisor test: F1=0.3052 F2=0.0874 G=0.3926 S=0.0000 T=1 G=41630398030028275444001574260091600 Main divisor test passed: 1/1 Final divisor test: F=0.3086 G=0.3926 H=1.0098 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec |
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(15*10^245-51)/99
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*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(15*10^583-51)/99
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*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=50*(10^1790-1)/33+1 [equals (15*10^1791-51)/99]
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== BPI:B2641040F9D72 ============================================ TITANIX 2.1.0 - Primality Certificate Started 07.23.2001 at 06:55:32 PM Running time 44h 38mn 27s Candidate certified prime ================================================================= Proved prime with Titanix by Hans Rosenthal. The zipped file "151_1061.zip" is 415 KB. When unpacked the file "Titanix-B2641040F9D72-001.out" is 962 KB and is available on demand by simple email request.
By Hans Rosenthal PFGW 1.1 test for probable primality in bases 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251 (15*10^7233-51)/99 is 3-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 5-PRP! (12.030000 seconds) (15*10^7233-51)/99 is 7-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 11-PRP! (11.980000 seconds) (15*10^7233-51)/99 is 13-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 17-PRP! (11.980000 seconds) (15*10^7233-51)/99 is 19-PRP! (11.980000 seconds) (15*10^7233-51)/99 is 23-PRP! (12.030000 seconds) (15*10^7233-51)/99 is 29-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 31-PRP! (11.920000 seconds) (15*10^7233-51)/99 is 37-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 41-PRP! (12.030000 seconds) (15*10^7233-51)/99 is 43-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 47-PRP! (11.970000 seconds) (15*10^7233-51)/99 is 53-PRP! (11.980000 seconds) (15*10^7233-51)/99 is 59-PRP! (11.980000 seconds) (15*10^7233-51)/99 is 61-PRP! (11.980000 seconds) (15*10^7233-51)/99 is 251-PRP! (11.970000 seconds)
By Hans Rosenthal PFGW 1.1 test for probable primality in bases 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, and 251 (15*10^24787-51)/99 is 3-PRP! (208.270000 seconds) (15*10^24787-51)/99 is 5-PRP! (203.990000 seconds) (15*10^24787-51)/99 is 7-PRP! (218.990000 seconds) (15*10^24787-51)/99 is 11-PRP! (208.720000 seconds) (15*10^24787-51)/99 is 13-PRP! (208.060000 seconds) (15*10^24787-51)/99 is 17-PRP! (214.430000 seconds) (15*10^24787-51)/99 is 19-PRP! (206.850000 seconds) (15*10^24787-51)/99 is 23-PRP! (209.370000 seconds) (15*10^24787-51)/99 is 29-PRP! (203.770000 seconds) (15*10^24787-51)/99 is 31-PRP! (207.790000 seconds) (15*10^24787-51)/99 is 37-PRP! (213.660000 seconds) (15*10^24787-51)/99 is 41-PRP! (210.690000 seconds) (15*10^24787-51)/99 is 43-PRP! (212.890000 seconds) (15*10^24787-51)/99 is 47-PRP! (202.130000 seconds) (15*10^24787-51)/99 is 53-PRP! (218.280000 seconds) (15*10^24787-51)/99 is 59-PRP! (210.200000 seconds) (15*10^24787-51)/99 is 61-PRP! (208.610000 seconds) (15*10^24787-51)/99 is 67-PRP! (204.760000 seconds) (15*10^24787-51)/99 is 71-PRP! (208.660000 seconds) (15*10^24787-51)/99 is 73-PRP! (216.960000 seconds) (15*10^24787-51)/99 is 79-PRP! (213.990000 seconds) (15*10^24787-51)/99 is 83-PRP! (210.750000 seconds) (15*10^24787-51)/99 is 89-PRP! (208.830000 seconds) (15*10^24787-51)/99 is 97-PRP! (216.410000 seconds) (15*10^24787-51)/99 is 101-PRP! (210.310000 seconds) (15*10^24787-51)/99 is 103-PRP! (212.170000 seconds) (15*10^24787-51)/99 is 107-PRP! (202.780000 seconds) (15*10^24787-51)/99 is 109-PRP! (213.660000 seconds) (15*10^24787-51)/99 is 113-PRP! (210.640000 seconds) (15*10^24787-51)/99 is 127-PRP! (207.230000 seconds) (15*10^24787-51)/99 is 251-PRP! (208.990000 seconds)
By Ray Chandler PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14] Primality testing (15*10^44653-51)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 19, base 1+sqrt(19) (15*10^44653-51)/99 is Fermat and Lucas PRP! (759.6120s+0.0025s)
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