(10^3-1)/3 - 2*(10^2+1)
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(13*10^3-31)/99
N=131
*** N is prime!
Time: 0 sec
(10^5-1)/3 - 2*(10^4+1)
run"aprt-cle
Test number N=? 13331
Preparatory test
Pass !
13331 is prime.
0:00:00
OK
Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.
(10^7-1)/3 - 2*(10^6+1)
run"aprt-cle
Test number N=? 1333331
Preparatory test
Pass !
1333331 is prime.
0:00:00
OK
Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.
(10^95-1)/3 - 2*(10^94+1)
== ID:B2869008C6612 =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 133333333333333333333333333333333333333333333333333333333333\
33333333333333333333333333333333331
Decimal size = 95
Binary size = 313
Started 01/26/2003 02:33:21 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.
(10^161-1)/3 - 2*(10^160+1)
== ID:B286903FE413A =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 133333333333333333333333333333333333333333333333333333333333\
333333333333333333333333333333333333333333333333333333333333\
33333333333333333333333333333333333333331
Decimal size = 161
Binary size = 532
Started 01/26/2003 06:36:34 PM
Running time 4s
Candidate certified prime
=================================================================
Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.
(10^361-1)/3 - 2*(10^360+1)
[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286A0111B6BE
Created=01/27/2003 04:58:58 AM
TestCount=51
Status=Candidate certified prime
[Candidate]
File=C:\Program Files\Primo200\pdp131_361.in
Expression=(10^361-1)/3 - 2*(10^(359+1)+1)
| N$=13D2DB934CBE6035AE5C48C0F4425C9378487DF0ADF21A1279E9770C93E488C4093C30F6099EB337D43A5E63CA7F2BEC\
A744B7C2FA2E4AC48DD57ED1902C1AB9F24D03D987732C967224C5880650388526832CEE27D8DA2992FFCEC3444FC007D7A\
BC2AC0D788A4081555555555555555555555555555555555555555555555555555555555555555555555555555555555555\
555553 |
HexadecimalSize=300
DecimalSize=361
BinarySize=1197
[Running Times]
Initialization=0.29s
1stPhase=2mn 8s
2ndPhase=27.86s
Total=2mn 36s
Proved prime with 'Primo 2.0.0 - beta 3'
by Patrick De Geest using a Pentium III 650 MHz chip.
(10^1471-1)/3 - 2*(10^1470+1)
C:\Pdp>pfgw -hhd1470.fac -l -tp -q"4*(10^1470-1)/3-1"
PFGW Version 1.1 for Windows
Output logging to file pfgw.out
Primality testing 4*(10^1470-1)/3-1 [N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file hd1470.fac
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling Brillhart-Lehmer-Selfridge with factored part 34.47%
4*(10^1470-1)/3-1 is prime! (8.010000 seconds)
Helper file and original proof by David Broadhurst.
Timing : reproduced on a Pentium III 650 MHz chip.
(10^2899-1)/3 - 2*(10^2898+1)
C:\Pdp>pfgw -hhd2898.fac -l -tp -q"4*(10^2898-1)/3-1"
PFGW Version 1.1 for Windows
Output logging to file pfgw.out
Primality testing 4*(10^2898-1)/3-1 [N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file hd2898.fac
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling Brillhart-Lehmer-Selfridge with factored part 33.46%
4*(10^2898-1)/3-1 is prime! (35.920000 seconds)
Helper file and original proof by David Broadhurst.
Timing : reproduced on a Pentium III 650 MHz chip.
Announced via
http://groups.yahoo.com/group/primenumbers/message/11084
(10^15699-1)/3 - 2*(10^15698+1)
3-PRP!
(10^17957-1)/3 - 2*(10^17956+1)
3-PRP!
(10^42263-1)/3 - 2*(10^42262+1)
3-PRP!
(10^111033-1)/3 - 2*(10^111032+1)
By Ray Chandler dd. April 15, 2011.
PFGW Version 3.4.6.64BIT.20110307.Win_Dev [GWNUM 26.5]
Primality testing (4*10^111032-7)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 31, base 2+sqrt(31)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.06% proof)
(4*10^111032-7)/3 is Fermat and Lucas PRP! (5052.1160s+7.9273s)
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( © All rights reserved ) - Last modified : March 15, 2023.
Patrick De Geest - Belgium 
- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com