== ID:B2813049EE978 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 777767777 Decimal size = 9 Binary size = 30 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 11/01/2002 09:32:03 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.
== ID:B2813049DC386 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 77777677777 Decimal size = 11 Binary size = 37 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 11/01/2002 09:30:48 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.
== ID:B2813049BED04 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 77777777677777777 Decimal size = 17 Binary size = 57 Started 11/01/2002 09:28:47 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.
== ID:B2813049A3DF6 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 77777777777677777777777 Decimal size = 23 Binary size = 77 Started 11/01/2002 09:26:57 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.
[PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B2800014790D6 Created=10/13/2002 05:57:47 AM TestCount=371 Status=Candidate certified prime [Running Times] Initialization=13.54s 1stPhase=52h 20mn 25s 2ndPhase=4h 4mn 24s Total=56h 25mn 3s Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen using a 1.33 GHz Athlon chip. The file "Primo-B2800014790D6-001.out" is 1042 KB and is available on demand by simple email request.
Darren Bedwell has a Primo certificate for 7*(10^3371-1)/9-10^1685. http://zerosink.blogspot.com/2010/10/primo-certificate-for-7103371-19-101685.html Certificate here [PRIMO - Primality Certificate] Version=3.0.9 WebSite=http://www.ellipsa.eu/ Format=3 ID=B3366018DAC88 Created=10/09/2010 07:14:28 AM TestCount=463 Status=Candidate certified prime [Comments] Write any comment here [Running Times] Initialization=6.81s 1stPhase=29h 3mn 43s 2ndPhase=8h 53mn 12s Total=37h 57mn 3s [Candidate] File=Z:\home\darren\Desktop\primo\work\77677.in Expression=7*(10^3371-1)/9-10^1685
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The near-repdigit palindrome wing prime 7*(10^4019-1)/9-10^2009 has been certified prime by Darren Bedwell using Primo and published dd. Oct 26, 2010. The certificate is here. [PRIMO - Primality Certificate] Version=3.0.9 WebSite=http://www.ellipsa.eu/ Format=3 ID=B336E027B2832 Created=10/17/2010 11:33:56 AM TestCount=593 Status=Candidate certified prime [Comments] Write any comment here [Running Times] Initialization=10.37s 1stPhase=53h 45mn 12s 2ndPhase=14h 18mn 42s Total=68h 4mn 4s [Candidate] File=Z:\home\darren\Desktop\primo\work\prp2009.in Expression=7*(10^4019-1)/9-10^2009
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C:\pfgw>pfgw64 -q"7*(10^29315-1)/9 - 10^14657" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] 7*(10^29315-1)/9 - 10^14657 is 3-PRP! (4.3185s+0.0011s)
C:\pfgw>pfgw64 -q"7*(10^30237-1)/9 - 10^15118" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] 7*(10^30237-1)/9 - 10^15118 is 3-PRP! (4.7284s+0.0010s)
C:\Users\Bob\Documents\IntSeq\Details>pfgw64 -q"(7*10^(2*20332+1)-9*10^20332-7)/9" -tc PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11] Primality testing (7*10^(2*20332+1)-9*10^20332-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.17% proof) (7*10^(2*20332+1)-9*10^20332-7)/9 is Fermat and Lucas PRP! (242.3012s+0.0118s)
pfgw64 -tc -q"(7*10^(2*50830+1)-9*10^50830-7)/9" PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11] Primality testing (7*10^(2*50830+1)-9*10^50830-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof) (7*10^(2*50830+1)-9*10^50830-7)/9 is Fermat and Lucas PRP! (1564.2487s+0.0560s)
pfgw64 -f0 -q"(7*10^(2*75062+1)-9*10^75062-7)/9" -tc PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11] No factoring at all, not even trivial division Primality testing (7*10^(2*75062+1)-9*10^75062-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N-1 test using base 7 Running N-1 test using base 11 Running N-1 test using base 13 Running N-1 test using base 17 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.02% proof) (7*10^(2*75062+1)-9*10^75062-7)/9 is Fermat and Lucas PRP! (6835.5344s+0.0236s)
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Patrick De Geest - Belgium
- Short Bio - Some PicturesE-mail address : pdg@worldofnumbers.com