*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(37*10^3-73)/99 N=373 *** N is prime! Time: 0 sec
== ID:B2814000E4606 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 3337333 Decimal size = 7 Binary size = 22 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 11/02/2002 12:15:35 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.
== ID:B2814000CCEFC ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 333333373333333 Decimal size = 15 Binary size = 49 Started 11/02/2002 12:13:59 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.
== ID:B2814000B9406 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 33333333333733333333333 Decimal size = 23 Binary size = 75 Started 11/02/2002 12:12:38 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.
== ID:B2814000A529E ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 333333333333373333333333333 Decimal size = 27 Binary size = 89 Started 11/02/2002 12:11:16 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.
== ID:B28140008B376 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 33333333333333333733333333333333333 Decimal size = 35 Binary size = 115 Started 11/02/2002 12:09:30 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.
== ID:B281400071070 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 33333333333333333333333333333733333333333333333333333333333 Decimal size = 59 Binary size = 195 Started 11/02/2002 12:07:42 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.
== ID:B281400050A50 =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333333333333333333333373333333333333333333333333333\
333
Decimal size = 63
Binary size = 208
Started 11/02/2002 12:05:30 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.
== ID:B28140003271C =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333333333333333333333333733333333333333333333333333\
3333333
Decimal size = 67
Binary size = 221
Started 11/02/2002 12:03:26 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.
== ID:B2814000159D2 =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333333333333333333333333333333333333333333333333333\
333333333333333337333333333333333333333333333333333333333333\
33333333333333333333333333333333333
Decimal size = 155
Binary size = 514
Started 11/02/2002 12:01:28 AM
Running time 3s
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 - (3)933 7 (3)933 Format=2 ID=B27F302916C46 Created=09/30/2002 11:58:04 AM TestCount=259 Status=Candidate certified prime [Running Times] Initialization=6.36s 1stPhase=14h 32mn 6s 2ndPhase=1h 1mn 6s Total=15h 33mn 19s Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen using a 1.33 GHz Athlon chip. The file "Primo-B27F302916C46-001.out" is 516KB and is available on demand by simple email request.
Darren Bedwell used Primo to prove this PWP prime. The certificates are posted to my weblog : Blog: Zero Sink Post: Primo Certificate for (10^3111-1)/3+4*10^1555 Link: http://zerosink.blogspot.com/2010/09/primo-certificate-for-103111-134101555.html [PRIMO - Primality Certificate] Version=3.0.9 WebSite=http://www.ellipsa.eu/ Format=3 ID=B3353030A2DD5 Created=09/20/2010 02:10:11 PM TestCount=446 Status=Candidate certified prime [Comments] Write any comment here [Running Times] Initialization=13.01s 1stPhase=29h 45mn 35s 2ndPhase=11h 10mn 54s Total=40h 56mn 43s [Candidate] File=C:\Documents and Settings\dbedwell\Desktop\primes\primo\work\pwps.in Expression=(10^3111-1)/3+4*10^1555
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C:\pfgw>pfgw64 -q"(10^23517-1)/3 + 4*10^11758" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] (10^23517-1)/3 + 4*10^11758 is 3-PRP! (2.8370s+0.0012s)
pfgw64 -tc -q"(10^(2*117707+1)+12*10^117707-1)/3" PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11] Primality testing (10^(2*117707+1)+12*10^117707-1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 5 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N+1 BLS with factored part 0.00% and helper 0.00% (0.01% proof) (10^(2*117707+1)+12*10^117707-1)/3 is Fermat and Lucas PRP! (9782.3159s+0.0118s)
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Patrick De Geest - Belgium
- Short Bio - Some PicturesE-mail address : pdg@worldofnumbers.com