(38*10^3-83)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(38*10^3-83)/99 N=383 *** N is prime! Time: 0 sec
(38*10^9-83)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(38*10^9-83)/99 N=383838383 *** N is prime! Time: 1 sec
(38*10^15-83)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(38*10^15-83)/99 N=383838383838383 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3^2 divides N + 1 Factor: 11 divides N - 1 Factor: 53 divides N + 1 Factor: 107 divides N + 1 Factorization results: F1=0.0920 F2=0.4054 F1=22 F2=816624 Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=383838383838381 Pass: 5^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=329119272615629 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=210023926703083 Pass: gcd(5^((N-1)/11) - 1, N) = 1: R20=270441632471066 Pass: gcd(U{(N+1)/53}, N) = 1: d=5 p=1 q=-1 R20=257734922813305 Pass: gcd(U{(N+1)/107}, N) = 1: d=5 p=1 q=-1 R20=231529459225001 BLS tests passed: F1=0.0920 F2=0.4054 Main divisor test: F1=0.0714 F2=0.4054 G=0.4768 S=0.0000 T=1 G=8982864 Main divisor test passed: 1/1 Final divisor test: F=0.4054 G=0.4768 H=1.2875 t=1 a=1 Final divisor test passed: 5/5 r=5 i=0 *** N is prime! Time: 0 sec
(38*10^17-83)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(38*10^17-83)/99 N=38383838383838383 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3^4 divides N - 1 Factor: 293 divides N + 1 Factor: 1201 divides N + 1 Factorization results: F1=0.1332 F2=0.4070 F1=162 F2=5630288 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=38383838383838381 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=11679695711985769 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=1025624004196152 Pass: 5^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/293}, N) = 1: d=5 p=1 q=-1 R20=1110538465011468 Pass: gcd(U{(N+1)/1201}, N) = 1: d=5 p=1 q=-1 R20=5618342141313697 BLS tests passed: F1=0.1332 F2=0.4070 Main divisor test: F1=0.1151 F2=0.4070 G=0.5221 S=0.0000 T=1 G=456053328 Main divisor test passed: 1/1 *** N is prime! Time: 0 sec
(38*10^21-83)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(38*10^21-83)/99 N=383838383838383838383 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3 divides N + 1 Factor: 61 divides N - 1 Factorization results: F1=0.1014 F2=0.0817 F1=122 F2=48 Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=83838383838383838381 Pass: 5^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=91814045040657809482 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=52770870753703102511 Pass: gcd(5^((N-1)/61) - 1, N) = 1: R20=3212258427456713509 BLS tests passed: F1=0.1014 F2=0.0817 APRCL test T=180 S=14739725 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=0 R20=1 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=1 R20=68484848484848484848 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=3 R20=56649333572410495487 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=0 R20=1 APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=83838383838383838382 APRCL main test (1 8) for p=2 q=61 not needed APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=0 R20=1 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=19336219336219336220 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=95260295260295260295 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=34310850439882697947 APRCL main test (2 8) for p=3 q=61 not needed APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=8 R20=35325456678208272472 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=1 R20=38273797327140678004 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=41801045600850911179 APRCL main test (3 8) for p=5 q=61 not needed APRCL tests for p=5 completed Main divisor test: F1=0.0867 F2=0.0817 G=0.5167 S=0.3483 T=180 G=43157914800 Main divisor test passed: 180/180 *** N is prime! Time: 0 sec
(38*10^57-83)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(38*10^57-83)/99 N=383838383838383838383838383838383838383838383838383838383 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3 divides N + 1 Factor: 83 divides N - 1 Factor: 131 divides N - 1 Factor: 401 divides N - 1 Factor: 797 divides N + 1 Factor: 6841 divides N + 1 Factorization results: F1=0.1227 F2=0.1488 F1=8720146 F2=261709296 Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=83838383838383838381 Pass: 5^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=36108191301624638424 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=97774450920459978656 Pass: gcd(5^((N-1)/83) - 1, N) = 1: R20=84013097498849607821 Pass: gcd(5^((N-1)/131) - 1, N) = 1: R20=27010660165567559006 Pass: gcd(5^((N-1)/401) - 1, N) = 1: R20=76958054234172316883 Pass: gcd(U{(N+1)/797}, N) = 1: d=5 p=1 q=-1 R20=70309238211336308680 Pass: gcd(U{(N+1)/6841}, N) = 1: d=5 p=1 q=-1 R20=83510359301039093206 BLS tests passed: F1=0.1227 F2=0.1488 APRCL test T=1260 S=42149997664775 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=0 R20=1 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=1 R20=48484848484848484848 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=3 R20=47713824636901559978 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=0 R20=1 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=24931117137513267585 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=1 R20=50197371818993440615 APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=0 R20=61660745299828355901 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=19336219336219336220 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=95260295260295260295 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=33398501140436624308 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=25484351713859910581 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=8 R20=23308349442620592231 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=44990361866997834882 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=1 R20=48384283735312907698 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=3 R20=68215589402666788091 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=66205033111145695483 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=13732173284294386941 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=48654734965266909242 APRCL tests for p=5 completed APRCL main test (4) at level 4 for p=7 APRCL L_7 condition satisfied APRCL tests for p=7 completed Main divisor test: F1=0.1173 F2=0.1488 G=0.5069 S=0.2408 T=1260 G=48096166764863317566399133200 Main divisor test passed: 1260/1260 *** N is prime! Time: 0 sec
(38*10^4233-83)/99 == ID:B270C04277A32 ============================================= PRIMO 1.1.0 - Primality Certificate Started 02.11.2002 07:22:05 PM Running time 994h 35mn 12s Started 03.25.2002 07:52:29 AM Running time 131h 26mn 10s Candidate certified prime ================================================================= +-----------------------------------------------------------------------+ | Cert_Val a "PRIMO/Titanix" certificate (.out file) validation program | | Version 1.94 Jim Fougeron, Using the Miracl big integer library | | Copyright, 2001 Jim Fougeron, Free usage rights granted to all | +-----------------------------------------------------------------------+ Processing file primo-b270c04277a32.out This Certificate is a PRIMO compatible certificate 1) EC Test ECtest1 != Ident, ECtest2= Ident Validated 5mn 14.440s 2) EC Test ECtest1 != Ident, ECtest2= Ident Validated 4mn 38.546s ... ... 603) N-1 Test B^(N-1)=1 gcd(B^S-1,N)=1 Validated 0.001s 604) SPP Test Trial-div to 848043 !Success!!! Validated 0.005s Prime number being certified was: N=(38*10^4233-83)/99 Certificate for this number was FULLY validated! Total time used to validate certificate: 12h 57mn 51.035s There were 604 steps in the primality proof. ================================================================= Proved prime with 'Primo 1.1.0' by Hans Rosenthal. The zipped file "181_2116.zip" is 1775 KB. When unpacked the file "Primo-B270C04277A32.out" is 4059 KB and is available on demand by simple email request. Hans Rosenthal, HansRosenthal@t-online.de, April 2, 2002.
(38*10^4335-83)/99 == ID:B273D03D35858 ============================================= PRIMO 1.2.2 - Primality Certificate Started 04.01.2002 05:49:42 PM Running time 1247h 0mn 14s Candidate certified prime ================================================================= +------------------------------------------------------------------------+ | 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-b273d03d35858.out This Certificate is a PRIMO compatible certificate 1) EC Test ECtest1 != Ident, ECtest2= Ident Validated 5mn 36.481s 2) EC Test ECtest1 != Ident, ECtest2= Ident Validated 5mn 34.506s ... 651) N+1 Test V[(N+1)/2]=0 gcd(V[S/2],N)=1 Validated 0.002s 652) SPP Test Trial-div to 26924 !Success!!! Validated 0.002s Prime number being certified was: N=(38*10^4335-83)/99 Certificate for this number was FULLY validated! Total time used to validate certificate: 15h 18mn 30.531s There were 652 steps in the primality proof ================================================================= Proved prime with 'Primo 1.2.2' by Hans Rosenthal. The zipped file "181_2167.zip" is 1961 KB. When unpacked the file "Primo-B273D03D35858.out" is 4474 KB and is available on demand by simple email request.
(38*10^13221-83)/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 (38*10^13221-83)/99 is 3-PRP! (49.380000 seconds) (38*10^13221-83)/99 is 5-PRP! (49.820000 seconds) (38*10^13221-83)/99 is 7-PRP! (49.320000 seconds) (38*10^13221-83)/99 is 11-PRP! (49.760000 seconds) (38*10^13221-83)/99 is 13-PRP! (49.320000 seconds) (38*10^13221-83)/99 is 17-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 19-PRP! (49.260000 seconds) (38*10^13221-83)/99 is 23-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 29-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 31-PRP! (49.210000 seconds) (38*10^13221-83)/99 is 37-PRP! (49.440000 seconds) (38*10^13221-83)/99 is 41-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 43-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 47-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 53-PRP! (49.270000 seconds) (38*10^13221-83)/99 is 59-PRP! (49.210000 seconds) (38*10^13221-83)/99 is 61-PRP! (49.210000 seconds) (38*10^13221-83)/99 is 251-PRP! (49.210000 seconds)
(38*10^26447-83)/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 (38*10^26447-83)/99 is 3-PRP! (303.130000 seconds) (38*10^26447-83)/99 is 5-PRP! (307.630000 seconds) (38*10^26447-83)/99 is 7-PRP! (304.340000 seconds) (38*10^26447-83)/99 is 11-PRP! (305.660000 seconds) (38*10^26447-83)/99 is 13-PRP! (312.080000 seconds) (38*10^26447-83)/99 is 17-PRP! (308.080000 seconds) (38*10^26447-83)/99 is 19-PRP! (306.930000 seconds) (38*10^26447-83)/99 is 23-PRP! (305.000000 seconds) (38*10^26447-83)/99 is 29-PRP! (303.360000 seconds) (38*10^26447-83)/99 is 31-PRP! (305.330000 seconds) (38*10^26447-83)/99 is 37-PRP! (305.330000 seconds) (38*10^26447-83)/99 is 41-PRP! (310.990000 seconds) (38*10^26447-83)/99 is 43-PRP! (305.550000 seconds) (38*10^26447-83)/99 is 47-PRP! (305.660000 seconds) (38*10^26447-83)/99 is 53-PRP! (303.800000 seconds) (38*10^26447-83)/99 is 59-PRP! (305.280000 seconds) (38*10^26447-83)/99 is 61-PRP! (307.200000 seconds) (38*10^26447-83)/99 is 67-PRP! (305.820000 seconds) (38*10^26447-83)/99 is 71-PRP! (305.720000 seconds) (38*10^26447-83)/99 is 73-PRP! (306.160000 seconds) (38*10^26447-83)/99 is 79-PRP! (304.940000 seconds) (38*10^26447-83)/99 is 83-PRP! (306.540000 seconds) (38*10^26447-83)/99 is 89-PRP! (306.370000 seconds) (38*10^26447-83)/99 is 97-PRP! (305.170000 seconds) (38*10^26447-83)/99 is 101-PRP! (302.750000 seconds) (38*10^26447-83)/99 is 103-PRP! (304.670000 seconds) (38*10^26447-83)/99 is 107-PRP! (304.340000 seconds) (38*10^26447-83)/99 is 109-PRP! (305.170000 seconds) (38*10^26447-83)/99 is 113-PRP! (305.490000 seconds) (38*10^26447-83)/99 is 127-PRP! (304.890000 seconds) (38*10^26447-83)/99 is 251-PRP! (303.630000 seconds)
(38*10^29897-83)/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 (38*10^29897-83)/99 is 3-PRP! (345.040000 seconds) (38*10^29897-83)/99 is 5-PRP! (341.530000 seconds) (38*10^29897-83)/99 is 7-PRP! (341.970000 seconds) (38*10^29897-83)/99 is 11-PRP! (346.410000 seconds) (38*10^29897-83)/99 is 13-PRP! (347.130000 seconds) (38*10^29897-83)/99 is 17-PRP! (342.460000 seconds) (38*10^29897-83)/99 is 19-PRP! (344.050000 seconds) (38*10^29897-83)/99 is 23-PRP! (342.140000 seconds) (38*10^29897-83)/99 is 29-PRP! (342.620000 seconds) (38*10^29897-83)/99 is 31-PRP! (343.120000 seconds) (38*10^29897-83)/99 is 37-PRP! (342.740000 seconds) (38*10^29897-83)/99 is 41-PRP! (345.040000 seconds) (38*10^29897-83)/99 is 43-PRP! (344.500000 seconds) (38*10^29897-83)/99 is 47-PRP! (345.040000 seconds) (38*10^29897-83)/99 is 53-PRP! (343.120000 seconds) (38*10^29897-83)/99 is 59-PRP! (345.310000 seconds) (38*10^29897-83)/99 is 61-PRP! (351.850000 seconds) (38*10^29897-83)/99 is 67-PRP! (343.780000 seconds) (38*10^29897-83)/99 is 71-PRP! (343.890000 seconds) (38*10^29897-83)/99 is 73-PRP! (343.660000 seconds) (38*10^29897-83)/99 is 79-PRP! (344.330000 seconds) (38*10^29897-83)/99 is 83-PRP! (343.010000 seconds) (38*10^29897-83)/99 is 89-PRP! (343.180000 seconds) (38*10^29897-83)/99 is 97-PRP! (344.210000 seconds) (38*10^29897-83)/99 is 101-PRP! (341.030000 seconds) (38*10^29897-83)/99 is 103-PRP! (343.340000 seconds) (38*10^29897-83)/99 is 107-PRP! (342.570000 seconds) (38*10^29897-83)/99 is 109-PRP! (342.620000 seconds) (38*10^29897-83)/99 is 113-PRP! (345.430000 seconds) (38*10^29897-83)/99 is 127-PRP! (343.010000 seconds) (38*10^29897-83)/99 is 251-PRP! (346.360000 seconds)
(38*10^91997-83)/99 Test by Ray Chandler PFGW Version 3.4.8.64BIT.20110617.Win_Dev [GWNUM 26.6] Primality testing (38*10^91997-83)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number Running N-1 test using base 5 Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number Running N-1 test using base 7 Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number Running N+1 test using discriminant 13, base 2+sqrt(13) Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof) (38*10^91997-83)/99 is Fermat and Lucas PRP! (4293.2813s+0.0028s)