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8*(10^3-1)/9 - (10^2+1) *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(78*10^3-87)/99 N=787 *** N is prime! Time: 0 sec
8*(10^5-1)/9 - (10^4+1) run"aprt-cle Test number N=? 78887 Preparatory test Pass ! 78887 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
8*(10^87-1)/9 - (10^86+1) == ID:B28690085E1B6 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 788888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888887 Decimal size = 87 Binary size = 289 Started 01/26/2003 02:26:14 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.
8*(10^113-1)/9 - (10^112+1) == ID:B28690351CC48 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 788888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888887 Decimal size = 113 Binary size = 376 Started 01/26/2003 03:28:12 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.
8*(10^171-1)/9 - (10^170+1) == ID:B286904009F20 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 788888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888887 Decimal size = 171 Binary size = 568 Started 01/26/2003 06:39:09 PM Running time 5s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
8*(10^567-1)/9 - (10^566+1) == ID:B286C03C47DCE ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 788888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888888888888888888888888888888888888888\ 888888888888888888888888887 Decimal size = 567 Binary size = 1884 Started 01/29/2003 05:33:28 PM Running time 12mn 28s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Patrick De Geest using a Pentium III 650 MHz chip.
8*(10^1689-1)/9 - (10^1688+1) [PRIMO - Primality Certificate] Version=2.1.1 WebSite=http://www.ellipsa.net/ Format=3 ID=B290B00657C49 Created=07/07/2003 01:50:55 AM TestCount=259 Status=Candidate certified prime [Running Times] Initialization=4.46s 1stPhase=11h 10mn 1s 2ndPhase=1h 25mn 43s Total=12h 35mn 48s [Candidate] File=C:\Primo IN & OUT files\PDP1689.in Expression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exadecimalSize=1403 DecimalSize=1689 BinarySize=5611 Proved prime with 'Primo 2.1.1' by Patrick De Geest using a 3000 MHz Pentium 4 cpu. Certificate Primo-B290B00657C49-01.out available by simple email request (332 KB).
8*(10^8903-1)/9 - (10^8902+1) 3-PRP!
8*(10^115811-1)/9 - (10^115810+1) Tested by Ray Chandler PFGW Version 3.4.8.64BIT.20110617.Win_Dev [GWNUM 26.6] Primality testing (71*10^115810-17)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Generic modular reduction using generic reduction Core2 type-1 FFT length 48K, Pass1=64, Pass2=768 on A 384719-bit number Running N-1 test using base 7 Generic modular reduction using generic reduction Core2 type-1 FFT length 48K, Pass1=64, Pass2=768 on A 384719-bit number Running N+1 test using discriminant 17, base 1+sqrt(17) Generic modular reduction using generic reduction Core2 type-1 FFT length 48K, Pass1=64, Pass2=768 on A 384719-bit number Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof) (71*10^115810-17)/9 is Fermat and Lucas PRP! (5003.3912s+0.0088s)