*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(75*10^3-57)/99 N=757 *** N is prime! Time: 0 sec
== ID:B2813040BF294 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 777777757777777 Decimal size = 15 Binary size = 50 Started 11/01/2002 06:51:31 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:B2813040A92B4 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 777777777777757777777777777 Decimal size = 27 Binary size = 90 Started 11/01/2002 06:50:01 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:B28130408DE1A =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777757\
777777777777777777777777777777777777777777777777777777777
Decimal size = 117
Binary size = 389
Started 11/01/2002 06:48:10 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:B2813040673FA =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777577777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
7777777777777777777
Decimal size = 259
Binary size = 861
Started 11/01/2002 06:45:31 PM
Running time 39s
Candidate certified prime
=================================================================
Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.
== ID:B280A00AEDC74 =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777777757777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777777777777777777777777777777777777\
777777777777777777777777777
Decimal size = 507
Binary size = 1684
Started 10/23/2002 03:10:59 AM
Running time 4mn 36s
Candidate certified prime
=================================================================
Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.
Darren Bedwell used Primo to prove this PWP prime. The certificates are posted to his weblog : Blog: Zero Sink Post: Primo certificate for (7*(10^3315-1)/9)-2*10^1657 Link: http://zerosink.blogspot.com/2010/09/primo-certificate-for-7103315-19.html [PRIMO - Primality Certificate] Version=3.0.9 WebSite=http://www.ellipsa.eu/ Format=3 ID=B3350033263DB Created=09/17/2010 02:54:11 PM TestCount=468 Status=Candidate certified prime [Comments] Write any comment here [Running Times] Initialization=15.57s 1stPhase=54h 34mn 50s 2ndPhase=15h 31mn 21s Total=70h 6mn 27s [Candidate] File=C:\Documents and Settings\dbedwell\Desktop\primes\primo\work\nearrep797.in Expression=(7*(10^3315-1)/9)-2*10^1657
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Darren Bedwell used Primo to prove this PWP prime. The certificates are posted to his weblog : Blog: Zero Sink Post: 7*(10^4489-1)/9-2*10^2244 is prime. Link: http://zerosink.blogspot.com/2010/11/7104489-19-2102244-is-prime.html [PRIMO - Primality Certificate] Version=3.0.9 WebSite=http://www.ellipsa.eu/ Format=3 ID=B337702A08104 Created=10/26/2010 12:15:08 PM TestCount=610 Status=Candidate certified prime [Comments] Write any comment here [Running Times] Initialization=32.90s 1stPhase=215h 50mn 58s 2ndPhase=66h 2mn 42s Total=281h 54mn 14s [Candidate] File=C:\Documents and Settings\dbedwell\Desktop\primes\primo\work\prp2244.in Expression=7*(10^4489-1)/9-2*10^2244
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Xinyao Chen informs me (May 19, 2022) that this number is now a proven palindromic wing prime. Proof was done by Masaki UKAI on January 23, 2020. See source at https://stdkmd.net/nrr/records.htm#nrpprime
C:\pfgw>pfgw64 -q"7*(10^15849-1)/9-2*10^7924" PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^15849-1)/9-2*10^7924 is 3-PRP! (1.8878s+0.0005s)
C:\pfgw>pfgw64 -q"7*(10^19807-1)/9-2*10^9903" PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^19807-1)/9-2*10^9903 is 3-PRP! (3.4874s+0.0005s)
C:\pfgw>pfgw64 -q"7*(10^23799-1)/9-2*10^11899" PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^23799-1)/9-2*10^11899 is 3-PRP! (5.2659s+0.0004s)
C:\pfgw>pfgw64 -q"7*(10^36315-1)/9-2*10^18157" PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^36315-1)/9-2*10^18157 is 3-PRP! (12.1503s+0.0006s)
C:\pfgw>pfgw64 -q"7*(10^37915-1)/9-2*10^18957" PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^37915-1)/9-2*10^18957 is 3-PRP! (13.7118s+0.0006s)
C:\pfgw>pfgw64 -q"7*(10^47331-1)/9-2*10^23665" PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^47331-1)/9-2*10^23665 is 3-PRP! (22.0199s+0.0007s)
Primality testing (7*10^(2*105609+1)-18*10^105609-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 19, base 3+sqrt(19) Calling N-1 BLS with factored part 0.00% and helper 0.00% (0.01% proof) (7*10^(2*105609+1)-18*10^105609-7)/9 is Fermat and Lucas PRP! (6983.3030s+0.0308s)
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Patrick De Geest - Belgium
- Short Bio - Some PicturesE-mail address : pdg@worldofnumbers.com