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2*(10^3-1)/9 + 5*(10^2+1) *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(72*10^3-27)/99 N=727 *** N is prime! Time: 0 sec
2*(10^5-1)/9 + 5*(10^4+1) run"aprt-cle Test number N=? 72227 Preparatory test Pass ! 72227 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^9-1)/9 + 5*(10^8+1) run"aprt-cle Test number N=? 722222227 Preparatory test Pass ! 722222227 is prime. 0:00:00 OK Proved prime with 'Ubasic - APRT-CLE.UB' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^29-1)/9 + 5*(10^28+1) == ID:B286500F8D284 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 72222222222222222222222222227 Decimal size = 29 Binary size = 96 ----------------------------------------------------------------- 1) N-1 Test ----------------------------------------------------------------- N = Candidate S = 24178 R = 2987104897932923410630417 B = 2 ----------------------------------------------------------------- 2) N+1 Test ----------------------------------------------------------------- N = R of preceding test S = 2 R = 1493552448966461705315209 Q = 14 ----------------------------------------------------------------- 3) EC Test ----------------------------------------------------------------- N = R of preceding test S = 7101297 R = 210321079229440261 A = 0 B = 16 T = 2 ----------------------------------------------------------------- 4) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 73980 R = 2842945109887 B = 2 ----------------------------------------------------------------- 5) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/22/2003 04:31:46 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.
2*(10^65-1)/9 + 5*(10^64+1) == ID:B2869006422BA ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 722222222222222222222222222222222222222222222222222222222222\ 22227 Decimal size = 65 Binary size = 216 Started 01/26/2003 01:49:22 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.
2*(10^725-1)/9 + 5*(10^724+1) [PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B286D03FF84FA Created=01/30/2003 06:37:57 PM TestCount=119 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\pdp727_725.in Expression=2*(10^725-1)/9 + 5*(10^(723+1)+1) N$=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 HexadecimalSize=602 DecimalSize=725 BinarySize=2408 [Running Times] Initialization=1.44s 1stPhase=1h 35mn 36s 2ndPhase=17mn 20s Total=1h 52mn 58s Proved prime with 'Primo 2.0.0 - beta 3' by Patrick De Geest using a Pentium III 650 MHz chip.
2*(10^1787-1)/9 + 5*(10^1786+1) [PRIMO - Primality Certificate] Version=2.1.1 WebSite=http://www.ellipsa.net/ Format=3 ID=B290C02E07C87 Created=07/08/2003 01:24:31 PM TestCount=253 Status=Candidate certified prime [Running Times] Initialization=5.11s 1stPhase=12h 13mn 36s 2ndPhase=50mn 19s Total=13h 4mn 1s [Candidate] File=C:\Primo IN & OUT files\PDP1787.in Expression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exadecimalSize=1484 DecimalSize=1787 BinarySize=5936 Proved prime with 'Primo 2.1.1' by Patrick De Geest using a 3000 MHz Pentium 4 cpu. Certificate Primo-B290C02E07C87-01.out available by simple email request (337 KB).
2*(10^7277-1)/9 + 5*(10^7276+1) 3-PRP!
2*(10^19463-1)/9 + 5*(10^19462+1) 3-PRP!
2*(10^24215-1)/9 + 5*(10^24214+1) 3-PRP! PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].
2*(10^51779-1)/9 + 5*(10^51778+1) PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14] Primality testing (65*10^51778+43)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) (65*10^51778+43)/9 is Fermat and Lucas PRP! (1532.2989s+0.0028s)