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(10^53-1) - 10^26 == ID:B2814010102EC ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 99999999999999999999999999899999999999999999999999999 Decimal size = 53 Binary size = 177 Started 11/02/2002 04:40:43 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.
(10^757-1) - 10^378 [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B2808009F5B3C Created=10/21/2002 02:54:03 AM TestCount=123 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\pwp989_757.in Expression=(10^757-1) - 10^378 N$=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 HexadecimalSize=629 DecimalSize=757 BinarySize=2515 [Running Times] Initialization=1.86s 1stPhase=36mn 38s 2ndPhase=4mn 42s Total=41mn 22s Proved prime with 'Primo 2.0.0 - beta 3' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^2493-1) - 10^1246 (9)1246 8 (9)1246 is prime, it is provable by a N+1 method. C:\PrimeForm>pfgw -q10^2493-10^1246-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^2493-10^1246-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.94% 10^2493-10^1246-1 is prime! (9.780000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^3597-1) - 10^1798 (9)1798 8 (9)1798 is prime, it is provable by a N+1 method. C:\PrimeForm>pfgw -q10^3597-10^1798-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^3597-10^1798-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.93% 10^3597-10^1798-1 is prime! (24.220000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^5835-1) - 10^2917 (9)2917 8 (9)2917 is prime, it is provable by a N+1 method. C:\PrimeForm>pfgw -q10^5835-10^2917-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^5835-10^2917-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.94% 10^5835-10^2917-1 is prime! (56.910000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^46069-1) - 10^23034 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/2364 C:\PrimeForm>pfgw -q10^46069-10^23034-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^46069-10^23034-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^46069-10^23034-1 is prime! (6449.950000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^95019-1) - 10^47509 Ref.: http://groups.yahoo.com/group/primeform/message/3008
http://groups.yahoo.com/group/primeform/message/3009
http://groups.yahoo.com/group/primeform/message/3010 PrimeForm Output C:\Pfgw4>pfgw -q"(10^95019-1)-10^47509" -tp PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (10^95019-1)-10^47509 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 2+sqrt(7) Running N+1 test using discriminant 7, base 7+sqrt(7) Running N+1 test using discriminant 7, base 8+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% (10^95019-1)-10^47509 is prime! (8769.3868s+0.0064s)
(10^104281-1) - 10^52140 Ref.: http://groups.yahoo.com/group/primeform/message/3033 PrimeForm Output C:\Pfgw4>pfgw -q"(10^104281-1)-10^52140" -tp PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (10^104281-1)-10^52140 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% (10^104281-1)-10^52140 is prime! (3130.3335s+0.0077s)
(10^134809-1) - 10^67404 By Darren Bedwell http://zerosink.blogspot.com/ Primality testing 10^(2*67404+1)-1*10^67404-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^(2*67404+1)-1*10^67404-1 is prime! (4490.0911s+0.0381s)