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(10^177-1) - 4*10^88 == ID:B280F00B775C8 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999959999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999 Decimal size = 177 Binary size = 588 Started 10/28/2002 03:20:23 AM Running time 4s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^225-1) - 4*10^112 == ID:B280F00B446B4 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999959999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999 Decimal size = 225 Binary size = 748 Started 10/28/2002 03:16:54 AM Running time 15s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^397-1) - 4*10^198 == ID:B280B00CD3EA8 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999599999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999\ 9999999999999999999999999999999999999 Decimal size = 397 Binary size = 1319 Started 10/24/2002 03:44:10 AM Running time 1mn 56s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^1245-1) - 4*10^622 [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 - (9)622 5 (9)622 Format=2 ID=B27F4033AC5DE Created=10/01/2002 03:03:03 PM TestCount=201 Status=Candidate certified prime [Running Times] Initialization=2.60s 1stPhase=2h 7mn 25s 2ndPhase=13mn 33s Total=2h 21mn 2s Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen using a 1.33 GHz Athlon chip. The file "Primo-B27F4033AC5DE-001.out" is 280 KB and is available on demand by simple email request.
(10^8457-1) - 4*10^4228 (9)4228 5 (9)4228 is prime, it is provable by a N+1 method. C:\PrimeForm>pfgw -q10^8457-4*10^4228-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^8457-4*10^4228-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Calling Brillhart-Lehmer-Selfridge with factored part 34.94% 10^8457-4*10^4228-1 is prime! (142.860000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^20105-1) - 4*10^10052 (9)10052 5 (9)10052 is prime, it is provable by a N+1 method. C:\PrimeForm>pfgw -q10^20105-4*10^10052-1 -tp PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor') Primality testing 10^20105-4*10^10052-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^20105-4*10^10052-1 is prime! (1077.740000 seconds) (Timing using a Pentium III 650 Mhz chip).
(10^111725-1) - 4*10^55862 5076a 10^111725-4*10^55862-1 111725 p235 2010 Near-repdigit, palindrome C:\Pfgw4>pfgw -q"10^111725-4*10^55862-1" -tp PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 10^111725-4*10^55862-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Running N+1 test using discriminant 11, base 2+sqrt(11) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^111725-4*10^55862-1 is prime! (6526.7481s+0.0082s)