== ID:B281003F50700 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 77477 Decimal size = 5 Binary size = 17 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 10/29/2002 06:26:29 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:B281003F3F34C ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 7774777 Decimal size = 7 Binary size = 23 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 10/29/2002 06:25:19 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:B281003F248C6 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 7777774777777 Decimal size = 13 Binary size = 43 ----------------------------------------------------------------- 1) SPP Test ----------------------------------------------------------------- N = Candidate Started 10/29/2002 06:23:30 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:B281003F07618 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 77777777777777777777777477777777777777777777777 Decimal size = 47 Binary size = 156 Started 10/29/2002 06:21:30 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:B281003EE7BF6 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 7777777777777777777777777777777777774777777777777777777777777777777777777 Decimal size = 73 Binary size = 243 Started 10/29/2002 06:19:20 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:B281003EC26E4 =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
777777777477777777777777777777777777777777777777777777777777\
7777777777777777777
Decimal size = 139
Binary size = 462
Started 10/29/2002 06:16:48 PM
Running time 2s
Candidate certified prime
=================================================================
Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.
== ID:B27F1031C53CE ============================================= PRIMO 1.2.1 - Primality Certificate - (7)561 4 (7)561 Started 09/28/2002 02:29:48 PM Running time 1h 20mn 28s Candidate certified prime ================================================================= Proved prime with 'Primo 1.2.1' by Jeff Heleen using a 1.33 GHz Athlon chip. The file "Primo-B27F1031C53CE.out" is 291 KB and is available on demand by simple email request.
[PRIMO - Primality Certificate] Version=2.0.0 - beta 3 - (7)723 4 (7)723 Format=2 ID=B27F40183CF1A Created=10/01/2002 07:03:35 AM TestCount=229 Status=Candidate certified prime [Running Times] Initialization=3.38s 1stPhase=4h 28mn 18s 2ndPhase=28mn 49s Total=4h 57mn 11s Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen using a 1.33 GHz Athlon chip. The file "Primo-B27F40183CF1A-001.out" is 373 KB and is available on demand by simple email request. Note : don't try to (re)certify this number with Primo 1.2.1 as this number will make the program 'freeze' (on a 1.33 Ghz Athlon PC after 1 hr 13 min 50 sec) at test 8, index = 18529. Marcel Martin found the bug, a vicious one, and he writes : " Under extremely rare circumstances, Primo 1.2.1 starts an infinite loop. In that case, the index value, in the Certification dialog box, doesn't progress any more and the only way to terminate the program is the use <CTRL-ALT-DEL>. This bug doesn't concern the registered version."
Xinyao Chen informs me (May 19,2022) that this number is now a proven palindromic wing prime. Proof was done by Maksym Voznyy on November 9, 2020. See source at https://stdkmd.net/nrr/records.htm#nrpprime
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^8209-1)/9-3*10^4104 is 3-PRP! (0.6231s+0.0011s)
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^18041-1)/9-3*10^9020 is 3-PRP! (3.6110s+0.0012s)
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^27955-1)/9-3*10^13977 is 3-PRP! (9.6308s+0.0014s)
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^39311-1)/9-3*10^19655 is 3-PRP! (20.6267s+0.0017s)
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6] 7*(10^64801-1)/9-3*10^32400 is 3-PRP! (53.0142s+0.0025s)
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Patrick De Geest - Belgium
- Short Bio - Some PicturesE-mail address : pdg@worldofnumbers.com