== ID:B281203AADF90 =============================================

PRIMO 1.2.1 - Primality Certificate

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Candidate
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N = 99999999999999499999999999999

Decimal size = 29
Binary size = 97

Started 10/31/2002 05:05:30 PM
Running time < 1s

Candidate certified prime

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

== ID:B281203A98096 =============================================

PRIMO 1.2.1 - Primality Certificate

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Candidate
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N = 999999999999999999999949999999999999999999999

Decimal size = 45
Binary size = 150

Started 10/31/2002 05:04:00 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:B2812039D0686 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
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N = 999999999999999999999999999999999999499999999999999999999999\
    9999999999999

Decimal size = 73
Binary size = 243

Started 10/31/2002 04:50:22 PM
Running time < 1s

Candidate certified prime

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

== ID:B28120399F61C =============================================

PRIMO 1.2.1 - Primality Certificate

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Candidate
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N = 999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999994999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    99999999999999999999999999999

Decimal size = 209
Binary size = 695

Started 10/31/2002 04:47:01 PM
Running time 11s

Candidate certified prime

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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)1136 4 (9)1136
Format=2
ID=B27FE014D7DF2
Created=10/11/2002 06:04:15 AM
TestCount=369
Status=Candidate certified prime

[Running Times]
Initialization=12.27s
1stPhase=41h 21mn 18s
2ndPhase=3h 17mn 17s
Total=44h 38mn 48s

Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen
using a 1.33 GHz Athlon chip.
The file "Primo-B27FE014D7DF2-001.out" is 980 KB
and is available on demand by simple email request.

The form of this prime is P = 10^(2n+1)-a*10^n-1 = 10^n(10^(n+1)-a)-1.
P+1 is "factorable" for 50%, so a N+1 methode is available
and PFGW (PrimeForm) can prove it.

C:\PrimeForm>pfgw -q10^35729-5*10^17864-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^35729-5*10^17864-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Running N+1 test using discriminant 3, base 3+sqrt(3)
Running N+1 test using discriminant 3, base 5+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^35729-5*10^17864-1 is prime! (11387.870000 seconds)

(Timing using a Pentium III 650 Mhz chip).

The form of this prime is P = 10^(2n+1)-a*10^n-1 = 10^n(10^(n+1)-a)-1.
P+1 is "factorable" for 50%, so a N+1 methode is available
and PFGW (PrimeForm) can prove it.

Ref.:
http://groups.yahoo.com/group/primeform/message/2403

C:\PrimeForm>pfgw -q10^50897-5*10^25448-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^50897-5*10^25448-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^50897-5*10^25448-1 is prime! (9740.210000 seconds)

(Timing using a Pentium III 650 Mhz chip).