7*(10^5-1)/9 - 3*10^2
== 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.


7*(10^7-1)/9 - 3*10^3
== 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.


7*(10^13-1)/9 - 3*10^6
== 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.


7*(10^47-1)/9 - 3*10^23
== 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.


7*(10^73-1)/9 - 3*10^36
== 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.


7*(10^139-1)/9 - 3*10^69
== 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.


7*(10^1123-1)/9 - 3*10^561
== 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.


7*(10^1447-1)/9 - 3*10^723
[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."


7*(10^6877-1)/9 - 3*10^3438
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


7*(10^8209-1)/9 - 3*10^4104
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)



7*(10^18041-1)/9 - 3*10^9020
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)



7*(10^27955-1)/9 - 3*10^13977
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)



7*(10^39311-1)/9 - 3*10^19655
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)



7*(10^64801-1)/9-3*10^32400
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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( © All rights reserved ) - Last modified : March 26, 2023.

Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com