== ID:B280F00B775C8 =============================================

PRIMO 1.2.1 - Primality Certificate

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Candidate
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N = 999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999959999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999

Decimal size = 177
Binary size = 588

Started 10/28/2002 03:20:23 AM
Running time 4s

Candidate certified prime

=================================================================

Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.

== ID:B280F00B446B4 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999959999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999

Decimal size = 225
Binary size = 748

Started 10/28/2002 03:16:54 AM
Running time 15s

Candidate certified prime

=================================================================

Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.

== ID:B280B00CD3EA8 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999599999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    9999999999999999999999999999999999999

Decimal size = 397
Binary size = 1319

Started 10/24/2002 03:44:10 AM
Running time 1mn 56s

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 - (9)622 5 (9)622
Format=2
ID=B27F4033AC5DE
Created=10/01/2002 03:03:03 PM
TestCount=201
Status=Candidate certified prime

[Running Times]
Initialization=2.60s
1stPhase=2h 7mn 25s
2ndPhase=13mn 33s
Total=2h 21mn 2s

Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen
using a 1.33 GHz Athlon chip.
The file "Primo-B27F4033AC5DE-001.out" is 280 KB
and is available on demand by simple email request.

(9)42285(9)4228 is prime, it is provable by a N+1 method.

C:\PrimeForm>pfgw -q10^8457-4*10^4228-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^8457-4*10^4228-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling Brillhart-Lehmer-Selfridge with factored part 34.94%
10^8457-4*10^4228-1 is prime! (142.860000 seconds)

(Timing using a Pentium III 650 Mhz chip).

(9)100525(9)10052 is prime, it is provable by a N+1 method.

C:\PrimeForm>pfgw -q10^20105-4*10^10052-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^20105-4*10^10052-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^20105-4*10^10052-1 is prime! (1077.740000 seconds)

(Timing using a Pentium III 650 Mhz chip).

5076a 10^111725-4*10^55862-1           111725 p235 2010 
          Near-repdigit, palindrome

C:\Pfgw4>pfgw -q"10^111725-4*10^55862-1" -tp
PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 10^111725-4*10^55862-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^111725-4*10^55862-1 is prime! (6526.7481s+0.0082s)