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2*(10^5-1)/3 - 5*(10^4+1) run"aprt-cle Test number N=? 16661 Preparatory test Pass ! 16661 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^13-1)/3 - 5*(10^12+1) run"aprt-cle Test number N=? 2*(10^13-1)\3 - 5*(10^12+1) Preparatory test Pass ! Main test for P= 2 for Q= 3 for Q= 5 for Q= 7 for Q= 13 for Q= 11 Main test for P= 3 for Q= 7 for Q= 13 Main test for P= 5 for Q= 11 Pass ! 1666666666661 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^17-1)/3 - 5*(10^16+1) == ID:B286400BEAF3C ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 16666666666666661 Decimal size = 17 Binary size = 54 ----------------------------------------------------------------- 1) N+1 Test ----------------------------------------------------------------- N = Candidate S = 6 R = 2777777777777777 Q = 3 ----------------------------------------------------------------- 2) N+1 Test ----------------------------------------------------------------- N = R of preceding test S = 124686 R = 22278185023 Q = 7 ----------------------------------------------------------------- 3) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/21/2003 03:28:16 AM Running time < 1s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^19-1)/3 - 5*(10^18+1) == ID:B286400C0B44E ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 1666666666666666661 Decimal size = 19 Binary size = 61 ----------------------------------------------------------------- 1) N+1 Test ----------------------------------------------------------------- N = Candidate S = 2094 R = 795924864692773 Q = 2 ----------------------------------------------------------------- 2) EC Test ----------------------------------------------------------------- N = R of preceding test S = 6122937 R = 129990691 A = 0 B = 4 T = 2 ----------------------------------------------------------------- 3) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/21/2003 03:30:29 AM Running time < 1s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^37-1)/3 - 5*(10^36+1) == ID:B2865010BF94A ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 1666666666666666666666666666666666661 Decimal size = 37 Binary size = 121 ----------------------------------------------------------------- 1) EC Test ----------------------------------------------------------------- N = Candidate S = 107511755169656392 R = 15502180799082133901 A =-1 B = 0 T = 2 ----------------------------------------------------------------- 2) N+1 Test ----------------------------------------------------------------- N = R of preceding test S = 35946858 R = 431252734219 Q = 2 ----------------------------------------------------------------- 3) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/22/2003 04:52:41 AM Running time < 1s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^53-1)/3 - 5*(10^52+1) == ID:B2868048CA95C ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 16666666666666666666666666666666666666666666666666661 Decimal size = 53 Binary size = 174 Started 01/25/2003 09:12:07 PM Running time < 1s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^73-1)/3 - 5*(10^72+1) == ID:B2869006E9E5C ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 166666666666666666666666666666666666666666666666666666666666\ 6666666666661 Decimal size = 73 Binary size = 240 Started 01/26/2003 02:00:49 AM Running time < 1s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^101-1)/3 - 5*(10^100+1) == ID:B286900941F60 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 166666666666666666666666666666666666666666666666666666666666\ 66666666666666666666666666666666666666661 Decimal size = 101 Binary size = 333 Started 01/26/2003 02:41:47 AM Running time < 1s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^6233-1)/3 - 5*(10^6232+1) 3-PRP!
2*(10^24029-1)/3 - 5*(10^24028+1) 3-PRP! PFGW Version 20040816.Win_Stable (v1.2 RC1a) [FFT v23.8]
2*(10^40223-1)/3 - 5*(10^40222+1) 3-PRP! PFGW Version 20040816.Win_Stable (v1.2 RC1a) [FFT v23.8]
2*(10^66395-1)/3 - 5*(10^66394+1) (5*10^66394-17)/3 is 3-PRP! (217.2589s+0.0029s) (5*10^66394-17)/3 is 23-PRP! (286.7449s+0.0033s) Re-confirmation with -tc: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (5*10^66394-17)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Running N+1 test using discriminant 11, base 3+sqrt(11) Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof) (5*10^66394-17)/3 is Fermat and Lucas PRP! (2667.8445s+0.0060s) Done.