loading...



















(10^3-1) - 8*10^1 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(91*10^3-19)/99 N=919 *** N is prime! Time: 0 sec
(10^11-1) - 8*10^5 == ID:B280C00F5A82A ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 99999199999 Decimal size = 11 Binary size = 37 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 10/25/2002 04:28:19 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.
(10^27-1) - 8*10^13 == ID:B280C00F2CA6A ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999919999999999999 Decimal size = 27 Binary size = 90 Started 10/25/2002 04:25:11 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.
(10^87-1) - 8*10^43 == ID:B280C00EEDDD8 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999919999999999999999\ 999999999999999999999999999 Decimal size = 87 Binary size = 290 Started 10/25/2002 04:20:54 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.
(10^339-1) - 8*10^169 == ID:B280C00EA709A ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999919999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999 Decimal size = 339 Binary size = 1127 Started 10/25/2002 04:16:04 AM Running time 1mn 3s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^363-1) - 8*10^181 == ID:B280B00D40AE4 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 919999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999 Decimal size = 363 Binary size = 1206 Started 10/24/2002 03:51:36 AM Running time 1mn 12s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^3159-1) - 8*10^1579 (9)1579 1 (9)1579 is prime, it is provable by a N+1 method. C:\PrimeForm>pfgw -q10^3159-8*10^1579-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^3159-8*10^1579-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.94% 10^3159-8*10^1579-1 is prime! (16.040000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^36155-1) - 8*10^18077 The form of this prime is P = 10^(2n+1)-a*10^n-1 = 10^n(10^(n+1)-a)-1. P+1 is "factorable" for 50%, so a N+1 methode is available and PFGW (PrimeForm) can prove it. C:\PrimeForm>pfgw -q10^36155-8*10^18077-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^36155-8*10^18077-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^36155-8*10^18077-1 is prime! (3683.970000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^45305-1) - 8*10^22652 The form of this prime is P = 10^(2n+1)-a*10^n-1 = 10^n(10^(n+1)-a)-1. P+1 is "factorable" for 50%, so a N+1 methode is available and PFGW (PrimeForm) can prove it. C:\PrimeForm>pfgw -q10^45305-8*10^22652-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^45305-8*10^22652-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^45305-8*10^22652-1 is prime! (6455.060000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^314727-1) - 8*10^157363 Primality testing 10^(2*157363+1)-8*10^157363-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Generic modular reduction using generic reduction AMD K10 type-1 FFT length 112K, Pass1=112, Pass2=1K on A 1045501-bit number Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^(2*157363+1)-8*10^157363-1 is prime! (39200.4130s+0.7439s) Top Twenty Palindromic Primes