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(78*10^3-87)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(78*10^3-87)/99 N=787 *** N is prime! Time: 0 sec
(78*10^5-87)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(78*10^5-87)/99 N=78787 *** N is prime! Time: 0 sec
(78*10^21-87)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(78*10^21-87)/99 N=787878787878787878787 Factor: 2 divides N - 1 Factor: 2^2 divides N + 1 Factor: 3 divides N - 1 Factor: 653 divides N - 1 Factor: 967 divides N - 1 Factorization results: F1=0.3148 F2=0.0288 F1=3788706 F2=4 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=87878787878787878785 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=72261441967267298276 Pass: gcd(3^((N-1)/653) - 1, N) = 1: R20=32332421815511943304 Pass: gcd(3^((N-1)/967) - 1, N) = 1: R20=89479634850406340140 BLS tests passed: F1=0.3148 F2=0.0288 APRCL test T=12 S=35 APRCL main test (1) at level 1 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=87878787878787878786 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=83636363636363636363 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1 APRCL tests for p=2 completed APRCL main test (2) at level 1 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 tests for p=3 completed Main divisor test: F1=0.3004 F2=0.0288 G=0.4031 S=0.0739 T=12 G=265209420 Main divisor test passed: 12/12 Final divisor test: F=0.3148 G=0.4031 H=1.0327 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec
(78*10^27-87)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(78*10^27-87)/99 N=787878787878787878787878787 Factor: 2 divides N - 1 Factor: 2^2 divides N + 1 Factor: 3 divides N - 1 Factor: 7307 divides N + 1 Factorization results: F1=0.0289 F2=0.1660 F1=6 F2=29228 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=87878787878787878785 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=98572212658718603580 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0 Pass: gcd(5^((N-1)/3) - 1, N) = 1: R20=65480855587662710716 Pass: 5^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/7307}, N) = 1: d=5 p=1 q=-1 R20=41108120264446100386 BLS tests passed: F1=0.0289 F2=0.1660 APRCL test T=180 S=899123225 APRCL main test (1) at level 3 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=87878787878787878786 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=63636363636363636363 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=5594405594405594405 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=87878787878787878786 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=3 R20=92696652089288477356 APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=87878787878787878786 APRCL tests for p=2 completed APRCL main test (2) at level 3 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=2 R20=87878787878787878784 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=2 R20=87878787878787878784 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=87878787878787878784 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=3 R20=16614364406731958847 APRCL tests for p=3 completed APRCL main test (3) at level 3 for p=5 APRCL L_5 condition satisfied APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=2 R20=92587027297771099424 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=79484753886418818781 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=4 R20=81796193594097383401 APRCL tests for p=5 completed Main divisor test: F1=0.0177 F2=0.1660 G=0.5167 S=0.3329 T=180 G=78838720860900 Main divisor test passed: 60/180 *** N is prime! Time: 0 sec
(78*10^95-87)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(78*10^95-87)/99 N=78787878787878787878787878787878787878787878787878787878787878787878787878787878787878787878787 Factor: 2 divides N - 1 Factor: 2^2 divides N + 1 Factor: 3^4 divides N - 1 Factor: 23 divides N + 1 Factor: 3467 divides N - 1 Factor: 33091 divides N + 1 Factorization results: F1=0.0606 F2=0.0683 F1=561654 F2=3044372 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=87878787878787878785 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=57237901962179769224 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0 Pass: gcd(5^((N-1)/3) - 1, N) = 1: R20=84164504975974825615 Pass: 5^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/23}, N) = 1: d=5 p=1 q=-1 R20=24861110972262906010 Pass: gcd(5^((N-1)/3467) - 1, N) = 1: R20=41161634633370851157 Pass: gcd(U{(N+1)/33091}, N) = 1: d=5 p=1 q=-1 R20=89543500525101488061 BLS tests passed: F1=0.0606 F2=0.0683 APRCL test T=2520 S=56325605729274370962234592119010146425 APRCL main test (1) at level 5 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=87878787878787878786 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=63636363636363636363 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=87878787878787878786 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=1864801864801864801 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=87878787878787878786 APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=87878787878787878786 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=0 R20=21903528702776216885 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=3 R20=95092635633176173716 APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=20638915636015846632 APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=0 R20=26977263719237559903 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=0 R20=1 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=87878787878787878786 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=87878787878787878786 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=1 R20=24929846418666725480 APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=1 R20=87878787878787878786 APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=7 R20=2994249454689668847 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=5 R20=60533274194373837834 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=5 R20=60244585646999496874 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=0 R20=83149324215648330686 APRCL tests for p=2 completed APRCL main test (2) at level 5 for p=3 APRCL L_3 condition satisfied APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=2 R20=87878787878787878784 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=87878787878787878784 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=87878787878787878784 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=2 R20=0 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=6 R20=87878787878787878780 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=2 R20=0 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=1 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=5 R20=0 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=1 R20=1 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=1 R20=1 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=0 R20=6 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=6 R20=87878787878787878780 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=7 R20=0 APRCL tests for p=3 completed APRCL main test (3) at level 5 for p=5 APRCL L_5 condition satisfied APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=1 R20=53668920611069371399 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=75048087535080251001 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=85691366771721515070 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=87713957745397567136 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=3 R20=41691463333994577795 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=2 R20=63000640487669080917 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=1 R20=84218286589069872847 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=0 R20=37009210451109582365 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=1 R20=43583364880211995024 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=0 R20=36221525547901860258 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=0 R20=26042391364844991587 APRCL tests for p=5 completed APRCL main test (4) at level 5 for p=7 APRCL L_7 condition satisfied APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=3 R20=88916016535025104462 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=0 R20=10653111923440322197 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=1 R20=89356521085358701414 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=4 R20=8377145792707238003 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=5 R20=69399618463530046444 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=0 R20=27353185954799300858 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=4 R20=1640995420112024389 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=6 R20=27804052396759792604 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=4 R20=328729913926784646 APRCL tests for p=7 completed Main divisor test: F1=0.0574 F2=0.0683 G=0.5235 S=0.3978 T=2520 G=48155117882458148604063672031073992673053652672700 Main divisor test passed: 2520/2520 *** N is prime! Time: 1 sec
(78*10^2075-87)/99 == BPI:B263C01D19308 ============================================ TITANIX 2.1.0 - Primality Certificate Started 07.18.2001 at 08:28:31 AM Running time 65h 13mn 12s Candidate certified prime ================================================================= Proved prime with Titanix by Hans Rosenthal. The zipped file "787_1037.zip" is 395 KB. When unpacked the file "Titanix-B263C01D19308-001.out" is 919 KB and is available on demand by simple email request.
(78*10^2165-87)/99 (78*10^2165-87)/99 == ID:B264E0446A380 ============================================= PRIMO 0.1.0 - Primality Certificate Started 08.05.2001 07:55:38 PM Running time 56h 49mn 43s Candidate certified prime ================================================================= Proved prime with 'Primo' by Hans Rosenthal. The zipped file "787_1082.zip" is 477 KB. When unpacked the file "Primo-B264E0446A380-001.out" is 1104 KB and is available on demand by simple email request.
(78*10^3047-87)/99 == ID:B266C0038C520 ============================================= PRIMO 0.1.0 - Primality Certificate Started 09.04.2001 01:02:00 AM Running time 179h 6mn 23s Candidate certified prime ================================================================= Proved prime with 'Primo' by Hans Rosenthal. The zipped file "787_1523.zip" is 909 KB. When unpacked the file "Primo-B266C0038C520-001.out" is 2079 KB and is available on demand by simple email request.
(78*10^3503-87)/99 == ID:B269801BB6D76 ============================================= PRIMO 1.1.0 - Primality Certificate Started 11.24.2001 09:00:16 PM Running time 420h 1mn 1s Started 12.10.2001 01:54:33 AM Running time 44h 15mn 33s Candidate certified prime ================================================================= Proved prime with 'Primo' by Hans Rosenthal. The zipped file "787_1751.zip" is 1150 KB. When unpacked the file "Primo-B269801BB6D76.out" is 2644 KB and is available on demand by simple email request.
(78*10^16791-87)/99 PFGW 1.1 test for probable primality in basis 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61, and 251 (78*10^16791-87)/99 is 3-PRP! (75.680000 seconds) (78*10^16791-87)/99 is 5-PRP! (77.780000 seconds) (78*10^16791-87)/99 is 7-PRP! (75.910000 seconds) (78*10^16791-87)/99 is 11-PRP! (75.690000 seconds) (78*10^16791-87)/99 is 13-PRP! (75.800000 seconds) (78*10^16791-87)/99 is 17-PRP! (75.910000 seconds) (78*10^16791-87)/99 is 19-PRP! (78.210000 seconds) (78*10^16791-87)/99 is 23-PRP! (75.800000 seconds) (78*10^16791-87)/99 is 29-PRP! (76.290000 seconds) (78*10^16791-87)/99 is 31-PRP! (76.460000 seconds) (78*10^16791-87)/99 is 37-PRP! (75.690000 seconds) (78*10^16791-87)/99 is 41-PRP! (83.980000 seconds) (78*10^16791-87)/99 is 43-PRP! (75.850000 seconds) (78*10^16791-87)/99 is 47-PRP! (75.850000 seconds) (78*10^16791-87)/99 is 53-PRP! (75.850000 seconds) (78*10^16791-87)/99 is 59-PRP! (78.870000 seconds) (78*10^16791-87)/99 is 61-PRP! (75.850000 seconds) (78*10^16791-87)/99 is 251-PRP! (77.880000 seconds)
(78*10^34883-87)/99 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 (78*10^34883-87)/99 is 3-PRP! (488.500000 seconds) (78*10^34883-87)/99 is 5-PRP! (505.650000 seconds) (78*10^34883-87)/99 is 7-PRP! (495.430000 seconds) (78*10^34883-87)/99 is 11-PRP! (494.390000 seconds) (78*10^34883-87)/99 is 13-PRP! (501.800000 seconds) (78*10^34883-87)/99 is 17-PRP! (496.470000 seconds) (78*10^34883-87)/99 is 19-PRP! (494.990000 seconds) (78*10^34883-87)/99 is 23-PRP! (488.120000 seconds) (78*10^34883-87)/99 is 29-PRP! (495.700000 seconds) (78*10^34883-87)/99 is 31-PRP! (494.210000 seconds) (78*10^34883-87)/99 is 37-PRP! (494.600000 seconds) (78*10^34883-87)/99 is 41-PRP! (496.520000 seconds) (78*10^34883-87)/99 is 43-PRP! (496.850000 seconds) (78*10^34883-87)/99 is 47-PRP! (501.200000 seconds) (78*10^34883-87)/99 is 53-PRP! (495.980000 seconds) (78*10^34883-87)/99 is 59-PRP! (498.940000 seconds) (78*10^34883-87)/99 is 61-PRP! (496.260000 seconds) (78*10^34883-87)/99 is 67-PRP! (493.890000 seconds) (78*10^34883-87)/99 is 71-PRP! (497.790000 seconds) (78*10^34883-87)/99 is 73-PRP! (493.840000 seconds) (78*10^34883-87)/99 is 79-PRP! (498.010000 seconds) (78*10^34883-87)/99 is 83-PRP! (503.450000 seconds) (78*10^34883-87)/99 is 89-PRP! (497.900000 seconds) (78*10^34883-87)/99 is 97-PRP! (494.880000 seconds) (78*10^34883-87)/99 is 101-PRP! (501.300000 seconds) (78*10^34883-87)/99 is 103-PRP! (492.020000 seconds) (78*10^34883-87)/99 is 107-PRP! (494.440000 seconds) (78*10^34883-87)/99 is 109-PRP! (492.960000 seconds) (78*10^34883-87)/99 is 113-PRP! (491.470000 seconds) (78*10^34883-87)/99 is 127-PRP! (503.390000 seconds) (78*10^34883-87)/99 is 251-PRP! (493.620000 seconds)