(32*10^5-23)/99
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(32*10^5-23)/99
N=32323
*** N is prime!
Time: 0 sec


(32*10^9-23)/99
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(32*10^9-23)/99
N=323232323
*** N is prime!
Time: 0 sec


(32*10^11-23)/99
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(32*10^11-23)/99
N=32323232323
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3^2 divides N - 1
Factor: 29 divides N - 1
Factor: 53 divides N + 1
Factor: 83 divides N - 1
Factorization results: F1=0.4412 F2=0.2214
F1=43326
F2=212
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=32323232321
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=16198539604
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=21870921832
Pass: gcd(3^((N-1)/29) - 1, N) = 1: R20=29159760567
Pass: gcd(U{(N+1)/53}, N) = 1: d=5 p=1 q=-1 R20=28402242962
Pass: gcd(3^((N-1)/83) - 1, N) = 1: R20=23942302048
BLS tests passed: F1=0.4412 F2=0.2214
Main divisor test: F1=0.4126 F2=0.2214 G=0.6339 S=0.0000 T=1
G=4592556
Main divisor test passed: 1/1
*** N is prime!
Time: 0 sec


(32*10^3015-23)/99
== ID:B265D044D8EA2 =============================================

PRIMO 0.1.0 - Primality Certificate

Started 08.20.2001 08:03:11 PM
Running time 290h 42mn 5s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "323_1507.zip" is 913 KB.
When unpacked the file "Primo-B265D044D8EA2-001.out" is 2092 KB
and is available on demand by simple email request.


(32*10^3407-23)/99
== ID:B268C0053A5D4 =============================================

PRIMO 1.0.0 - Primality Certificate

Started 10.06.2001 01:31:51 AM
Running time 273h 17mn 24s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "323_1703.zip" is 1181 KB.
When unpacked the file "Primo-B268C0053A5D4-S.out" is 2690 KB
and is available on demand by simple email request.

(32*10^6959-23)/99

Hans Rosenthal dd. July 13, 2003
announced via a message in Number Theory List (NMBRTHRY@LISTSERV.NODAK.EDU)
that this SUPP is prime !
He thereby also established a new Primo ECPP world record
performed on a single monoprocessor computersystem.

[PRIMO - Task Report]
Version=2.0.0 - beta 4
Task=Certification
ID=B290404F2E14A
Created=06.30.2003 11:03:46 PM

[Common]
Path=C:\Programme\Primo\Work\
Selected=1
Processed=1
Certified=1
Candidate #1=Certified, 5459h 25mn 0s

[Candidate #1]
Input=Primo-B276304567D8C-001.tmp Output=Primo-B276304567D8C-001.out
Status=Candidate certified prime

Proved prime with 'Primo 2.0.0 - beta 4'
by Hans Rosenthal using an Athlon 1.4 GHz. Running time
amounts to approximately 527 days (18 months). He thereby
established a new current ECPP (Elliptic Curve Primality
Proving) record !

Primality certificate available by clicking the following link :
https://www.ellipsa.eu/public/primo/files/ecpp6959.zip
A diary written by Hans Rosenthal can be consulted at
http://www.ellipsa.net/primo/ecpp6959_diary.txt (broken link)


The verification of the certificate was done with the same
Primo 2.0.0 beta 4 on the same Athlon 1.4 GHz and took
50.6 hours.

[PRIMO - Task Report]
Version=2.0.0 - beta 4
Task=Verification
ID=B290C04024258
Created=07.08.2003 06:40:56 PM

[Common]
Path=C:\Programme\Primo\Work\
Selected=1
Processed=1
Valid=1
Certificate #1=Valid, 50h 38mn 36s

[Certificate #1]
Output=ecpp6959.out
Status=Valid certificate


(32*10^9599-23)/99
From: Hans Rosenthal
Sent: Sun 21/10/12 03:19
Subject: SUPP (32*10^9599-23)/99 is prime.

Dear Patrick,

After 293 days (32*10^9599-23)/99 has now been certified prime with Primo. 

Best regards, Hans.

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

PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251

(32*10^9599-23)/99 is 3-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 5-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 7-PRP! (19.170000 seconds)
(32*10^9599-23)/99 is 11-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 13-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 17-PRP! (19.120000 seconds)
(32*10^9599-23)/99 is 19-PRP! (19.170000 seconds)
(32*10^9599-23)/99 is 23-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 29-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 31-PRP! (19.120000 seconds)
(32*10^9599-23)/99 is 37-PRP! (19.170000 seconds)
(32*10^9599-23)/99 is 41-PRP! (19.170000 seconds)
(32*10^9599-23)/99 is 43-PRP! (19.120000 seconds)
(32*10^9599-23)/99 is 47-PRP! (19.110000 seconds)
(32*10^9599-23)/99 is 53-PRP! (19.170000 seconds)
(32*10^9599-23)/99 is 59-PRP! (19.120000 seconds)
(32*10^9599-23)/99 is 61-PRP! (19.120000 seconds)
(32*10^9599-23)/99 is 251-PRP! (19.110000 seconds)


(32*10^11399-23)/99
By Hans Rosenthal

PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251

(32*10^11399-23)/99 is 3-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 5-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 7-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 11-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 13-PRP! (30.320000 seconds)
(32*10^11399-23)/99 is 17-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 19-PRP! (30.320000 seconds)
(32*10^11399-23)/99 is 23-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 29-PRP! (30.380000 seconds)
(32*10^11399-23)/99 is 31-PRP! (30.380000 seconds)
(32*10^11399-23)/99 is 37-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 41-PRP! (30.420000 seconds)
(32*10^11399-23)/99 is 43-PRP! (30.380000 seconds)
(32*10^11399-23)/99 is 47-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 53-PRP! (30.370000 seconds)
(32*10^11399-23)/99 is 59-PRP! (30.430000 seconds)
(32*10^11399-23)/99 is 61-PRP! (30.380000 seconds)
(32*10^11399-23)/99 is 251-PRP! (30.320000 seconds)


(32*10^16593-23)/99
By Hans Rosenthal

PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251

(32*10^16593-23)/99 is 3-PRP! (76.240000 seconds)
(32*10^16593-23)/99 is 5-PRP! (75.080000 seconds)
(32*10^16593-23)/99 is 7-PRP! (75.190000 seconds)
(32*10^16593-23)/99 is 11-PRP! (76.900000 seconds)
(32*10^16593-23)/99 is 13-PRP! (74.870000 seconds)
(32*10^16593-23)/99 is 17-PRP! (76.510000 seconds)
(32*10^16593-23)/99 is 19-PRP! (74.870000 seconds)
(32*10^16593-23)/99 is 23-PRP! (75.470000 seconds)
(32*10^16593-23)/99 is 29-PRP! (76.730000 seconds)
(32*10^16593-23)/99 is 31-PRP! (74.860000 seconds)
(32*10^16593-23)/99 is 37-PRP! (75.790000 seconds)
(32*10^16593-23)/99 is 41-PRP! (74.970000 seconds)
(32*10^16593-23)/99 is 43-PRP! (74.800000 seconds)
(32*10^16593-23)/99 is 47-PRP! (75.800000 seconds)
(32*10^16593-23)/99 is 53-PRP! (77.340000 seconds)
(32*10^16593-23)/99 is 59-PRP! (76.570000 seconds)
(32*10^16593-23)/99 is 61-PRP! (76.020000 seconds)
(32*10^16593-23)/99 is 251-PRP! (75.030000 seconds)


(32*10^25883-23)/99
By Hans Rosenthal

PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,
71,73,79,83,89,97,101,103,107,109,113,127 and 251

(32*10^25883-23)/99 is 3-PRP! (299.180000 seconds)
(32*10^25883-23)/99 is 5-PRP! (296.650000 seconds)
(32*10^25883-23)/99 is 7-PRP! (298.020000 seconds)
(32*10^25883-23)/99 is 11-PRP! (297.860000 seconds)
(32*10^25883-23)/99 is 13-PRP! (295.550000 seconds)
(32*10^25883-23)/99 is 17-PRP! (296.650000 seconds)
(32*10^25883-23)/99 is 19-PRP! (296.430000 seconds)
(32*10^25883-23)/99 is 23-PRP! (297.590000 seconds)
(32*10^25883-23)/99 is 29-PRP! (297.200000 seconds)
(32*10^25883-23)/99 is 31-PRP! (297.310000 seconds)
(32*10^25883-23)/99 is 37-PRP! (296.870000 seconds)
(32*10^25883-23)/99 is 41-PRP! (295.880000 seconds)
(32*10^25883-23)/99 is 43-PRP! (296.220000 seconds)
(32*10^25883-23)/99 is 47-PRP! (296.380000 seconds)
(32*10^25883-23)/99 is 53-PRP! (296.320000 seconds)
(32*10^25883-23)/99 is 59-PRP! (298.360000 seconds)
(32*10^25883-23)/99 is 61-PRP! (296.330000 seconds)
(32*10^25883-23)/99 is 67-PRP! (296.270000 seconds)
(32*10^25883-23)/99 is 71-PRP! (300.010000 seconds)
(32*10^25883-23)/99 is 73-PRP! (296.320000 seconds)
(32*10^25883-23)/99 is 79-PRP! (297.040000 seconds)
(32*10^25883-23)/99 is 83-PRP! (297.640000 seconds)
(32*10^25883-23)/99 is 89-PRP! (295.830000 seconds)
(32*10^25883-23)/99 is 97-PRP! (298.140000 seconds)
(32*10^25883-23)/99 is 101-PRP! (300.060000 seconds)
(32*10^25883-23)/99 is 103-PRP! (297.480000 seconds)
(32*10^25883-23)/99 is 107-PRP! (297.090000 seconds)
(32*10^25883-23)/99 is 109-PRP! (302.150000 seconds)
(32*10^25883-23)/99 is 113-PRP! (297.360000 seconds)
(32*10^25883-23)/99 is 127-PRP! (297.090000 seconds)
(32*10^25883-23)/99 is 251-PRP! (300.170000 seconds)
 

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