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5*(10^3-1)/9 - 2*(10^2+1) *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(35*10^3-53)/99 N=353 *** N is prime! Time: 0 sec
5*(10^9-1)/9 - 2*(10^8+1) run"aprt-cle Test number N=? 355555553 Preparatory test Pass ! 355555553 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
5*(10^141-1)/9 - 2*(10^140+1) == ID:B28690376117A ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 355555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555553 Decimal size = 141 Binary size = 467 Started 01/26/2003 04:07:49 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.
5*(10^231-1)/9 - 2*(10^230+1) == ID:B286A000468C0 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 355555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555553 Decimal size = 231 Binary size = 766 Started 01/27/2003 12:04:48 AM Running time 16s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
5*(10^427-1)/9 - 2*(10^426+1) [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B286B0165464E Created=01/28/2003 06:30:14 AM TestCount=74 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\pwp353_427.in Expression=5*(10^427-1)/9 - 2*(10^(425+1)+1) N$=1F5F714A5D852E5F79795F19A9173F558224BEF41086AC365B0016449A443E3E8CA2DDD70EEA1C8670AAF714A0915D3905399F2663AD523FCB830929F5353459C3784E259272468A0A962587BA47C9F87495DDF1844ABB5F3F87E1120FDD5FD3033A2929459B4AF454E4DB82BAF3CF009475396B99CB23EC0C9C55C0E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E1 HexadecimalSize=355 DecimalSize=427 BinarySize=1417 [Running Times] Initialization=0.36s 1stPhase=1mn 38s 2ndPhase=28.50s Total=2mn 7s Proved prime with 'Primo 2.0.0 - beta 3' by Patrick De Geest using a Pentium III 650 MHz chip.
5*(10^463-1)/9 - 2*(10^462+1) == ID:B286C01100300 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 355555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 555555555555555555555555555555555555555555555555555555555555\ 5555555555555555555555555555555555555555553 Decimal size = 463 Binary size = 1537 Started 01/29/2003 04:57:06 AM Running time 6mn 52s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
5*(10^727-1)/9 - 2*(10^726+1) [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B286E00DB01D2 Created=01/31/2003 03:59:12 AM TestCount=129 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\pdp353_727.in Expression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exadecimalSize=604 DecimalSize=727 BinarySize=2414 [Running Times] Initialization=1.73s 1stPhase=2h 10mn 2s 2ndPhase=10mn 9s Total=2h 20mn 14s Proved prime with 'Primo 2.0.0 - beta 3' by Patrick De Geest using a Pentium III 650 MHz chip.
5*(10^1975-1)/9 - 2*(10^1974+1) 32*(10^1974-1)9+1 was the largest proven plateau prime known in May 2001. In base 10, it consists of 1973 successive 5's sandwiched by a pair of 3's. C:\Pdp>pfgw -hhd1974.fac -l -tm -q"32*(10^1974-1)/9+1" PFGW Version 1.1 for Windows Output logging to file pfgw.out Primality testing 32*(10^1974-1)/9+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file hd1974.fac Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 32*(10^1974-1)/9+1 is prime! (6.430000 seconds) Helper file and proof by David Broadhurst. Timing : reproduced on a Pentium III 650 MHz chip. Compare the timings with this newly created Primo Certificate ! [PRIMO - Primality Certificate] Version=2.1.1 WebSite=http://www.ellipsa.net/ Format=3 ID=B290D009E7A50 Created=07/09/2003 02:53:12 AM TestCount=274 Status=Candidate certified prime [Running Times] Initialization=6.51s 1stPhase=21h 5mn 58s 2ndPhase=2h 7mn 17s Total=23h 13mn 22s [Candidate] File=C:\Primo IN & OUT files\PDP1975.in Expression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exadecimalSize=1640 DecimalSize=1975 BinarySize=6560 Proved prime with 'Primo 2.1.1' by Patrick De Geest using a 3000 MHz Pentium 4 cpu. Certificate Primo-B290D009E7A50-01.out available by simple email request (414 KB).
5*(10^7231-1)/9 - 2*(10^7230+1) 3-PRP!
5*(10^45861-1)/9 - 2*(10^45860+1) 3-PRP! PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].
5*(10^47305-1)/9 - 2*(10^47304+1) 3-PRP! PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].