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(10^3-1)/3 - 2*(10^2+1) *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(13*10^3-31)/99 N=131 *** N is prime! Time: 0 sec
(10^5-1)/3 - 2*(10^4+1) run"aprt-cle Test number N=? 13331 Preparatory test Pass ! 13331 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^7-1)/3 - 2*(10^6+1) run"aprt-cle Test number N=? 1333331 Preparatory test Pass ! 1333331 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^95-1)/3 - 2*(10^94+1) == ID:B2869008C6612 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 133333333333333333333333333333333333333333333333333333333333\ 33333333333333333333333333333333331 Decimal size = 95 Binary size = 313 Started 01/26/2003 02:33:21 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.
(10^161-1)/3 - 2*(10^160+1) == ID:B286903FE413A ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 133333333333333333333333333333333333333333333333333333333333\ 333333333333333333333333333333333333333333333333333333333333\ 33333333333333333333333333333333333333331 Decimal size = 161 Binary size = 532 Started 01/26/2003 06:36:34 PM Running time 4s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^361-1)/3 - 2*(10^360+1) [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B286A0111B6BE Created=01/27/2003 04:58:58 AM TestCount=51 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\pdp131_361.in Expression=(10^361-1)/3 - 2*(10^(359+1)+1) N$=13D2DB934CBE6035AE5C48C0F4425C9378487DF0ADF21A1279E9770C93E488C4093C30F6099EB337D43A5E63CA7F2BECA744B7C2FA2E4AC48DD57ED1902C1AB9F24D03D987732C967224C5880650388526832CEE27D8DA2992FFCEC3444FC007D7ABC2AC0D788A4081555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 HexadecimalSize=300 DecimalSize=361 BinarySize=1197 [Running Times] Initialization=0.29s 1stPhase=2mn 8s 2ndPhase=27.86s Total=2mn 36s Proved prime with 'Primo 2.0.0 - beta 3' by Patrick De Geest using a Pentium III 650 MHz chip.
(10^1471-1)/3 - 2*(10^1470+1) C:\Pdp>pfgw -hhd1470.fac -l -tp -q"4*(10^1470-1)/3-1" PFGW Version 1.1 for Windows Output logging to file pfgw.out Primality testing 4*(10^1470-1)/3-1 [N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file hd1470.fac Running N+1 test using discriminant 17, base 1+sqrt(17) Calling Brillhart-Lehmer-Selfridge with factored part 34.47% 4*(10^1470-1)/3-1 is prime! (8.010000 seconds) Helper file and original proof by David Broadhurst. Timing : reproduced on a Pentium III 650 MHz chip.
(10^2899-1)/3 - 2*(10^2898+1) C:\Pdp>pfgw -hhd2898.fac -l -tp -q"4*(10^2898-1)/3-1" PFGW Version 1.1 for Windows Output logging to file pfgw.out Primality testing 4*(10^2898-1)/3-1 [N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file hd2898.fac Running N+1 test using discriminant 17, base 1+sqrt(17) Calling Brillhart-Lehmer-Selfridge with factored part 33.46% 4*(10^2898-1)/3-1 is prime! (35.920000 seconds) Helper file and original proof by David Broadhurst. Timing : reproduced on a Pentium III 650 MHz chip. Announced via http://groups.yahoo.com/group/primenumbers/message/11084
(10^3095-1)/3 - 2*(10^3094+1) [PRIMO - Primality Certificate] Version=2.1.1 WebSite=http://www.ellipsa.net/ Format=3 ID=B292502F7CCCA Created=08/02/2003 01:50:15 PM TestCount=447 Status=Candidate certified prime [Running Times] Initialization=21.05s 1stPhase=262h 0mn 59s 2ndPhase=14h 1mn 58s Total=276h 3mn 19s [Candidate] File=C:\Primo IN & OUT files\PDP3095.in Expression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exadecimalSize=2570 DecimalSize=3095 BinarySize=10279 --------------------------------------------------------- [PRIMO - Task Report] Version=2.2.0 beta 1 WebSite=http://www.ellipsa.net/ Task=Verification ID=B29440369E817 Created=09/02/2003 03:54:32 PM [Common] Path=C:\Primo IN & OUT files\ Selected=1 Processed=1 Valid=1 Certificate #1=Valid, 2h 19mn 22s [Certificate #1] Input=Primo-B292502F7CCCA-01.out Status=Valid certificate --------------------------------------------------------- Proved prime with 'Primo 2.1.1' by Patrick De Geest using a 3000 MHz Pentium 4 cpu. Certificate Primo-B292502F7CCCA-01.out available by simple email request (1095 KB).
(10^3113-1)/3 - 2*(10^3112+1) [PRIMO - Primality Certificate] Version=2.2.0 beta 1 WebSite=http://www.ellipsa.net/ Format=3 ID=B29370332744A Created=08/20/2003 02:54:33 PM TestCount=437 Status=Candidate certified prime [Running Times] Initialization=34.86s 1stPhase=153h 56mn 51s 2ndPhase=36h 26mn 30s Total=190h 23mn 56s [Candidate] File=C:\Primo IN & OUT files\PDP3113.in Expression=(10^3113-1)/3-2*(10^3112+1) N$=4C63417D3F8B3E4D83700495FEBF5EBF564C2386850CB23A9822C215B252049F5AB9BB80E02E4E28906F58947748F28CA32B4FEAE6B4E52165137FA41B7B2E9AAC3DFED0F392EC9F6CDE5F7DA4EC464CC6A4758CF9EE243ADF57FB67938143FE0C6F37D2495E45B6579E110B05DA42988801C9F08765D5D51765E46977EC3D9639A94164C604902B3333B591540AF496BD20E123C4E178C3612CDFC58C670FEB1A2F87DDECEE3750F822B36093CB838F9F8DE7787C1E2401302FF52A19A896F0F51DAC2423ECFC006DA3635D10673CF00C38E1D4327319B09E1AEFE4E3298EA13D056D09428E7652AB912293806F5E799BAED8D8AA74A013A549391EDD13936A650A28B899B4C373E29010F4B9D384A007BFCE7EC247A5DF2A9DBE591C7248E5A06D90588B9AFCA811BAB9F8FD78803091D9BA82C2059BFD8626842D0B00B1B4500AB76C28FB75B7318BB38614E0856D52F4492F3664A5709AEA8C3E14010899CB35E58032661468A8CB012213DF7EAB2D1957524DA63318E233D01D8FD03AACFB0A9C40B55DA29B77955F0EA49255D41118D1642D6C82D17EA1BF602D0CD2A3745B714AB6CF0EEBAF49FCD0B7B064DCCF5F95B25E964FF911886F01EFA9AA5734946ACA974DA07804738F587A4BF8337F24A00205200F7FE2109BB9E510B51CA69EA225A781D36085E6E2C53F8DA06B05C4F9C4327A8BFD8D9D921F68F2F7993E85F9DA2FE1979B42429A34BBE7B517E9F4300ABA247DC935CB8EDD7BA065182AF9AEA435BE28EABFF1249F12063778729248357BF9A6B4E3319C5E34AF95FD1D788E0A5A60C914BCEC3E3F37D059042BD52601ECA52B43C3975419534F4B8CE557F15A757192F5FBB71BF8641BCCC0ADE8077E15B38E3DED3A6D00B83B93B5D766AC2C57725215608B7A29EF61296F229579A8F71688C183F6C10DE6AE5CFA7184EA40788525905AD1EFABD6C892AC1D83ED8042DA6BDAE8EFA807700E86969EFC08A79F40AB4C822D1F4151B3BB2C3583CB543CD8C8CEF75595E0083E54B8897D5D9CB6EED1F48CD1A8B358867F0F38B9611CF32E84C686E89C759D87D04BF389BBD6033D978D765AB67316BE8AE73693C5B8C701EA39839B76DE65B5DF8FC1851F564095263295DC07DDDE8CFE46996E463B0C6006D6C27BA0B9250C55D8083A5373EA5AC8FADCCD00EFB5FF97CD3C7C75CE3FAB0745BFF8A944CF617EEF4D550D06311C26E13C38A42E8510F6F580A28B6831DF03DD7546DE67F9428AD6474AECF69B25C815555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 HexadecimalSize=2585 DecimalSize=3113 BinarySize=10339 --------------------------------------------------------- [PRIMO - Task Report] Version=2.2.0 beta 1 WebSite=http://www.ellipsa.net/ Task=Verification ID=B295603A55922 Created=09/20/2003 04:59:27 PM [Common] Path=C:\Primo IN & OUT files\ Selected=1 Processed=1 Valid=1 Certificate #1=Valid, 3h 24mn 13s [Certificate #1] Input=Primo-B29370332744A-01.out Status=Valid certificate --------------------------------------------------------- Proved prime with 'Primo 2.2.0 - beta 1' by Patrick De Geest using a 3000 MHz Pentium 4 cpu. Certificate Primo-B29370332744A-01.out available by simple email request (1089 KB).
(10^15699-1)/3 - 2*(10^15698+1) 3-PRP!
(10^17957-1)/3 - 2*(10^17956+1) 3-PRP!
(10^42263-1)/3 - 2*(10^42262+1) 3-PRP!
(10^111033-1)/3 - 2*(10^111032+1) by Ray Chandler PFGW Version 3.4.6.64BIT.20110307.Win_Dev [GWNUM 26.5] Primality testing (4*10^111032-7)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 31, base 2+sqrt(31) Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.06% proof) (4*10^111032-7)/3 is Fermat and Lucas PRP! (5052.1160s+7.9273s)