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7*(10^7-1)/9 - 6*(10^6+1) run"aprt-cle Test number N=? 1777771 Preparatory test Pass ! 1777771 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
7*(10^49-1)/9 - 6*(10^48+1) == ID:B286501165296 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 1777777777777777777777777777777777777777777777771 Decimal size = 49 Binary size = 161 ----------------------------------------------------------------- 1) EC Test ----------------------------------------------------------------- N = Candidate S = 667203784048 R = 2664519926718342504627184075295192647 A =-35 B = 98 T = 1 ----------------------------------------------------------------- 2) EC Test ----------------------------------------------------------------- N = R of preceding test S = 300684 R = 8861528803389413816240533028047 A = 0 B = 8 T = 1 ----------------------------------------------------------------- 3) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 6 R = 1476921467231568969373422171341 B = 2 ----------------------------------------------------------------- 4) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 691578749020 R = 2135579598598766917 B = 2 ----------------------------------------------------------------- 5) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 774475644 R = 2757452239 B = 2 ----------------------------------------------------------------- 6) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/22/2003 05:04:00 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.
7*(10^103-1)/9 - 6*(10^102+1) == ID:B286903492426 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 177777777777777777777777777777777777777777777777777777777777\ 7777777777777777777777777777777777777777771 Decimal size = 103 Binary size = 340 Started 01/26/2003 03:18:45 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.
7*(10^193-1)/9 - 6*(10^192+1) == ID:B2869040322FE ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 177777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 7777777777771 Decimal size = 193 Binary size = 639 Started 01/26/2003 06:41:54 PM Running time 7s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
7*(10^367-1)/9 - 6*(10^366+1) == ID:B286A011D9C54 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 177777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 777777777777777777777777777777777777777777777777777777777777\ 7777771 Decimal size = 367 Binary size = 1217 Started 01/27/2003 05:11:57 AM Running time 4mn 51s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
7*(10^1003-1)/9 - 6*(10^1002+1) [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B286603C0C4FE Created=01/23/2003 05:29:24 PM TestCount=148 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\d1003.in Expression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exadecimalSize=833 DecimalSize=1003 BinarySize=3330 [Running Times] Initialization=1.38s 1stPhase=1h 26mn 31s 2ndPhase=10mn 12s Total=1h 36mn 45s [Backtrack Report] File=C:\Program Files\Primo200\Primo-B286603C0C4FE-001.br Proved prime with 'Primo 2.0.0 - beta 3' by David Broadhurst. The Primo certificate of the above PDP (the file is 148 KB) is available on demand by simple email request.
7*(10^20365-1)/9 - 6*(10^20364+1) 3-PRP! PFGW Version 20040816.Win_Stable (v1.2 RC1a) [FFT v23.8]
7*(10^37447-1)/9 - 6*(10^37446+1) 3-PRP! PFGW Version 20040816.Win_Stable (v1.2 RC1a) [FFT v23.8]
7*(10^56083-1)/9 - 6*(10^56082+1) (16*10^56082-61)/9 is 3-PRP! (199.1310s+0.0043s) Using the -tc switch PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (16*10^56082-61)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.04% proof) (16*10^56082-61)/9 is Fermat and Lucas PRP! (1087.4648s+0.0122s)