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(10^29-1) - 5*10^14 == ID:B281203AADF90 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 99999999999999499999999999999 Decimal size = 29 Binary size = 97 Started 10/31/2002 05:05:30 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.
(10^45-1) - 5*10^22 == ID:B281203A98096 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999949999999999999999999999 Decimal size = 45 Binary size = 150 Started 10/31/2002 05:04:00 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.
(10^73-1) - 5*10^36 == ID:B2812039D0686 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999499999999999999999999999\ 9999999999999 Decimal size = 73 Binary size = 243 Started 10/31/2002 04:50:22 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.
(10^209-1) - 5*10^104 == ID:B28120399F61C ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999994999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 99999999999999999999999999999 Decimal size = 209 Binary size = 695 Started 10/31/2002 04:47:01 PM Running time 11s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^2273-1) - 5*10^1136 [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 - (9)1136 4 (9)1136 Format=2 ID=B27FE014D7DF2 Created=10/11/2002 06:04:15 AM TestCount=369 Status=Candidate certified prime [Running Times] Initialization=12.27s 1stPhase=41h 21mn 18s 2ndPhase=3h 17mn 17s Total=44h 38mn 48s Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen using a 1.33 GHz Athlon chip. The file "Primo-B27FE014D7DF2-001.out" is 980 KB and is available on demand by simple email request.
(10^35729-1) - 5*10^17864 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 -q10^35729-5*10^17864-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^35729-5*10^17864-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Running N+1 test using discriminant 3, base 3+sqrt(3) Running N+1 test using discriminant 3, base 5+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^35729-5*10^17864-1 is prime! (11387.870000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^50897-1) - 5*10^25448 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. Ref.: http://groups.yahoo.com/group/primeform/message/2403
http://groups.yahoo.com/group/primeform/message/2404
http://groups.yahoo.com/group/primeform/message/2405 C:\PrimeForm>pfgw -q10^50897-5*10^25448-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^50897-5*10^25448-1 [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% 10^50897-5*10^25448-1 is prime! (9740.210000 seconds) (Timing using a Pentium III 650 Mhz chip).