*** 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

*** 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

*** 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

== ID:B265D044D8EA2 ============================================= PRIMO 0.1.0 - Primality Certificate Started 08.20.2001 08:03:11 PM Running time 290h 42mn 5sCandidate 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.

== ID:B268C0053A5D4 ============================================= PRIMO 1.0.0 - Primality Certificate Started 10.06.2001 01:31:51 AM Running time 273h 17mn 24sCandidate 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.

Hans Rosenthal dd. July 13, 2003 announced via a message in Number Theory List (NMBRTHRY@LISTSERV.NODAK.EDU) that this |

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 beencertified primewith 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)

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)

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)

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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