```

(38*10^3-83)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(38*10^3-83)/99
N=383
*** N is prime!
Time: 0 sec

(38*10^9-83)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(38*10^9-83)/99
N=383838383
*** N is prime!
Time: 1 sec

(38*10^15-83)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(38*10^15-83)/99
N=383838383838383
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3^2 divides N + 1
Factor: 11 divides N - 1
Factor: 53 divides N + 1
Factor: 107 divides N + 1
Factorization results: F1=0.0920 F2=0.4054
F1=22
F2=816624
Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=383838383838381
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=329119272615629
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=210023926703083
Pass: gcd(5^((N-1)/11) - 1, N) = 1: R20=270441632471066
Pass: gcd(U{(N+1)/53}, N) = 1: d=5 p=1 q=-1 R20=257734922813305
Pass: gcd(U{(N+1)/107}, N) = 1: d=5 p=1 q=-1 R20=231529459225001
BLS tests passed: F1=0.0920 F2=0.4054
Main divisor test: F1=0.0714 F2=0.4054 G=0.4768 S=0.0000 T=1
G=8982864
Main divisor test passed: 1/1
Final divisor test: F=0.4054 G=0.4768 H=1.2875 t=1 a=1
Final divisor test passed: 5/5 r=5 i=0
*** N is prime!
Time: 0 sec

(38*10^17-83)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(38*10^17-83)/99
N=38383838383838383
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3^4 divides N - 1
Factor: 293 divides N + 1
Factor: 1201 divides N + 1
Factorization results: F1=0.1332 F2=0.4070
F1=162
F2=5630288
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=38383838383838381
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=11679695711985769
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0
Pass: gcd(5^((N-1)/3) - 1, N) = 1: R20=1025624004196152
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/293}, N) = 1: d=5 p=1 q=-1 R20=1110538465011468
Pass: gcd(U{(N+1)/1201}, N) = 1: d=5 p=1 q=-1 R20=5618342141313697
BLS tests passed: F1=0.1332 F2=0.4070
Main divisor test: F1=0.1151 F2=0.4070 G=0.5221 S=0.0000 T=1
G=456053328
Main divisor test passed: 1/1
*** N is prime!
Time: 0 sec

(38*10^21-83)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(38*10^21-83)/99
N=383838383838383838383
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3 divides N + 1
Factor: 61 divides N - 1
Factorization results: F1=0.1014 F2=0.0817
F1=122
F2=48
Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=83838383838383838381
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=91814045040657809482
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=52770870753703102511
Pass: gcd(5^((N-1)/61) - 1, N) = 1: R20=3212258427456713509
BLS tests passed: F1=0.1014 F2=0.0817
APRCL test
T=180
S=14739725
APRCL main test (1) at level 3 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=1 R20=68484848484848484848
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=56649333572410495487
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=0 R20=1
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=83838383838383838382
APRCL main test (1 8) for p=2 q=61 not needed
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=0 R20=1
APRCL tests for p=2 completed
APRCL main test (2) at level 3 for p=3
APRCL L_3 condition satisfied
APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=1 R20=19336219336219336220
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=95260295260295260295
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=34310850439882697947
APRCL main test (2 8) for p=3 q=61 not needed
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=8 R20=35325456678208272472
APRCL tests for p=3 completed
APRCL main test (3) at level 3 for p=5
APRCL L_5 condition satisfied
APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=1 R20=38273797327140678004
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=41801045600850911179
APRCL main test (3 8) for p=5 q=61 not needed
APRCL tests for p=5 completed
Main divisor test: F1=0.0867 F2=0.0817 G=0.5167 S=0.3483 T=180
G=43157914800
Main divisor test passed: 180/180
*** N is prime!
Time: 0 sec

(38*10^57-83)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(38*10^57-83)/99
N=383838383838383838383838383838383838383838383838383838383
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3 divides N + 1
Factor: 83 divides N - 1
Factor: 131 divides N - 1
Factor: 401 divides N - 1
Factor: 797 divides N + 1
Factor: 6841 divides N + 1
Factorization results: F1=0.1227 F2=0.1488
F1=8720146
F2=261709296
Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=83838383838383838381
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=36108191301624638424
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=97774450920459978656
Pass: gcd(5^((N-1)/83) - 1, N) = 1: R20=84013097498849607821
Pass: gcd(5^((N-1)/131) - 1, N) = 1: R20=27010660165567559006
Pass: gcd(5^((N-1)/401) - 1, N) = 1: R20=76958054234172316883
Pass: gcd(U{(N+1)/797}, N) = 1: d=5 p=1 q=-1 R20=70309238211336308680
Pass: gcd(U{(N+1)/6841}, N) = 1: d=5 p=1 q=-1 R20=83510359301039093206
BLS tests passed: F1=0.1227 F2=0.1488
APRCL test
T=1260
S=42149997664775
APRCL main test (1) at level 4 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=1 R20=48484848484848484848
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=47713824636901559978
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=0 R20=1
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=0 R20=1
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=1 R20=24931117137513267585
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=0 R20=1
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=1 R20=50197371818993440615
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=0 R20=61660745299828355901
APRCL tests for p=2 completed
APRCL main test (2) at level 4 for p=3
APRCL L_3 condition satisfied
APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=1 R20=19336219336219336220
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=95260295260295260295
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=33398501140436624308
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=25484351713859910581
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=8 R20=23308349442620592231
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=44990361866997834882
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=1 R20=48384283735312907698
APRCL tests for p=3 completed
APRCL main test (3) at level 4 for p=5
APRCL L_5 condition satisfied
APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=3 R20=68215589402666788091
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=66205033111145695483
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=13732173284294386941
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=48654734965266909242
APRCL tests for p=5 completed
APRCL main test (4) at level 4 for p=7
APRCL L_7 condition satisfied
APRCL tests for p=7 completed
Main divisor test: F1=0.1173 F2=0.1488 G=0.5069 S=0.2408 T=1260
G=48096166764863317566399133200
Main divisor test passed: 1260/1260
*** N is prime!
Time: 0 sec

(38*10^4233-83)/99

== ID:B270C04277A32 =============================================

PRIMO 1.1.0 - Primality Certificate

Started 02.11.2002 07:22:05 PM
Running time 994h 35mn 12s
Started 03.25.2002 07:52:29 AM
Running time 131h 26mn 10s

Candidate certified prime

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

+-----------------------------------------------------------------------+
| Cert_Val a "PRIMO/Titanix" certificate (.out file) validation program |
|    Version 1.94 Jim Fougeron, Using the Miracl big integer library    |
|    Copyright, 2001 Jim Fougeron, Free usage rights granted to all     |
+-----------------------------------------------------------------------+

Processing file primo-b270c04277a32.out

This Certificate is a PRIMO compatible certificate

1) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 5mn 14.440s
2) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 4mn 38.546s
...
...
603) N-1 Test B^(N-1)=1 gcd(B^S-1,N)=1		Validated 0.001s
604) SPP Test Trial-div to 848043  !Success!!!	Validated 0.005s

Prime number being certified was:
N=(38*10^4233-83)/99

Certificate for this number was FULLY validated!
Total time used to validate certificate: 12h 57mn 51.035s
There were 604 steps in the primality proof.

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

Proved prime with 'Primo 1.1.0' by Hans Rosenthal.
The zipped file "181_2116.zip" is 1775 KB.
When unpacked the file "Primo-B270C04277A32.out" is 4059 KB
and is available on demand by simple email request.

Hans Rosenthal, HansRosenthal@t-online.de, April 2, 2002.

(38*10^4335-83)/99

== ID:B273D03D35858 =============================================

PRIMO 1.2.2 - Primality Certificate

Started 04.01.2002 05:49:42 PM
Running time 1247h 0mn 14s

Candidate certified prime

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

+------------------------------------------------------------------------+
| Cert_Val a "PRIMO/Titanix" certificate (.out file) validation program  |
|    Version 1.95 Jim Fougeron, Using the Miracl big integer library     |
|  Copyright, 2001-2002 Jim Fougeron, Free usage rights granted to all   |
+------------------------------------------------------------------------+

Processing file primo-b273d03d35858.out

This Certificate is a PRIMO compatible certificate

1) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 5mn 36.481s
2) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 5mn 34.506s
...
651) N+1 Test V[(N+1)/2]=0 gcd(V[S/2],N)=1	Validated 0.002s
652) SPP Test Trial-div to 26924  !Success!!!	Validated 0.002s

Prime number being certified was:
N=(38*10^4335-83)/99

Certificate for this number was FULLY validated!
Total time used to validate certificate: 15h 18mn 30.531s
There were 652 steps in the primality proof

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

Proved prime with 'Primo 1.2.2' by Hans Rosenthal.
The zipped file "181_2167.zip" is 1961 KB.
When unpacked the file "Primo-B273D03D35858.out" is 4474 KB
and is available on demand by simple email request.

(38*10^13221-83)/99

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

(38*10^13221-83)/99 is 3-PRP! (49.380000 seconds)
(38*10^13221-83)/99 is 5-PRP! (49.820000 seconds)
(38*10^13221-83)/99 is 7-PRP! (49.320000 seconds)
(38*10^13221-83)/99 is 11-PRP! (49.760000 seconds)
(38*10^13221-83)/99 is 13-PRP! (49.320000 seconds)
(38*10^13221-83)/99 is 17-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 19-PRP! (49.260000 seconds)
(38*10^13221-83)/99 is 23-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 29-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 31-PRP! (49.210000 seconds)
(38*10^13221-83)/99 is 37-PRP! (49.440000 seconds)
(38*10^13221-83)/99 is 41-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 43-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 47-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 53-PRP! (49.270000 seconds)
(38*10^13221-83)/99 is 59-PRP! (49.210000 seconds)
(38*10^13221-83)/99 is 61-PRP! (49.210000 seconds)
(38*10^13221-83)/99 is 251-PRP! (49.210000 seconds)

(38*10^26447-83)/99

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

(38*10^26447-83)/99 is 3-PRP! (303.130000 seconds)
(38*10^26447-83)/99 is 5-PRP! (307.630000 seconds)
(38*10^26447-83)/99 is 7-PRP! (304.340000 seconds)
(38*10^26447-83)/99 is 11-PRP! (305.660000 seconds)
(38*10^26447-83)/99 is 13-PRP! (312.080000 seconds)
(38*10^26447-83)/99 is 17-PRP! (308.080000 seconds)
(38*10^26447-83)/99 is 19-PRP! (306.930000 seconds)
(38*10^26447-83)/99 is 23-PRP! (305.000000 seconds)
(38*10^26447-83)/99 is 29-PRP! (303.360000 seconds)
(38*10^26447-83)/99 is 31-PRP! (305.330000 seconds)
(38*10^26447-83)/99 is 37-PRP! (305.330000 seconds)
(38*10^26447-83)/99 is 41-PRP! (310.990000 seconds)
(38*10^26447-83)/99 is 43-PRP! (305.550000 seconds)
(38*10^26447-83)/99 is 47-PRP! (305.660000 seconds)
(38*10^26447-83)/99 is 53-PRP! (303.800000 seconds)
(38*10^26447-83)/99 is 59-PRP! (305.280000 seconds)
(38*10^26447-83)/99 is 61-PRP! (307.200000 seconds)
(38*10^26447-83)/99 is 67-PRP! (305.820000 seconds)
(38*10^26447-83)/99 is 71-PRP! (305.720000 seconds)
(38*10^26447-83)/99 is 73-PRP! (306.160000 seconds)
(38*10^26447-83)/99 is 79-PRP! (304.940000 seconds)
(38*10^26447-83)/99 is 83-PRP! (306.540000 seconds)
(38*10^26447-83)/99 is 89-PRP! (306.370000 seconds)
(38*10^26447-83)/99 is 97-PRP! (305.170000 seconds)
(38*10^26447-83)/99 is 101-PRP! (302.750000 seconds)
(38*10^26447-83)/99 is 103-PRP! (304.670000 seconds)
(38*10^26447-83)/99 is 107-PRP! (304.340000 seconds)
(38*10^26447-83)/99 is 109-PRP! (305.170000 seconds)
(38*10^26447-83)/99 is 113-PRP! (305.490000 seconds)
(38*10^26447-83)/99 is 127-PRP! (304.890000 seconds)
(38*10^26447-83)/99 is 251-PRP! (303.630000 seconds)

(38*10^29897-83)/99

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

(38*10^29897-83)/99 is 3-PRP! (345.040000 seconds)
(38*10^29897-83)/99 is 5-PRP! (341.530000 seconds)
(38*10^29897-83)/99 is 7-PRP! (341.970000 seconds)
(38*10^29897-83)/99 is 11-PRP! (346.410000 seconds)
(38*10^29897-83)/99 is 13-PRP! (347.130000 seconds)
(38*10^29897-83)/99 is 17-PRP! (342.460000 seconds)
(38*10^29897-83)/99 is 19-PRP! (344.050000 seconds)
(38*10^29897-83)/99 is 23-PRP! (342.140000 seconds)
(38*10^29897-83)/99 is 29-PRP! (342.620000 seconds)
(38*10^29897-83)/99 is 31-PRP! (343.120000 seconds)
(38*10^29897-83)/99 is 37-PRP! (342.740000 seconds)
(38*10^29897-83)/99 is 41-PRP! (345.040000 seconds)
(38*10^29897-83)/99 is 43-PRP! (344.500000 seconds)
(38*10^29897-83)/99 is 47-PRP! (345.040000 seconds)
(38*10^29897-83)/99 is 53-PRP! (343.120000 seconds)
(38*10^29897-83)/99 is 59-PRP! (345.310000 seconds)
(38*10^29897-83)/99 is 61-PRP! (351.850000 seconds)
(38*10^29897-83)/99 is 67-PRP! (343.780000 seconds)
(38*10^29897-83)/99 is 71-PRP! (343.890000 seconds)
(38*10^29897-83)/99 is 73-PRP! (343.660000 seconds)
(38*10^29897-83)/99 is 79-PRP! (344.330000 seconds)
(38*10^29897-83)/99 is 83-PRP! (343.010000 seconds)
(38*10^29897-83)/99 is 89-PRP! (343.180000 seconds)
(38*10^29897-83)/99 is 97-PRP! (344.210000 seconds)
(38*10^29897-83)/99 is 101-PRP! (341.030000 seconds)
(38*10^29897-83)/99 is 103-PRP! (343.340000 seconds)
(38*10^29897-83)/99 is 107-PRP! (342.570000 seconds)
(38*10^29897-83)/99 is 109-PRP! (342.620000 seconds)
(38*10^29897-83)/99 is 113-PRP! (345.430000 seconds)
(38*10^29897-83)/99 is 127-PRP! (343.010000 seconds)
(38*10^29897-83)/99 is 251-PRP! (346.360000 seconds)

(38*10^91997-83)/99

Test by Ray Chandler

PFGW Version 3.4.8.64BIT.20110617.Win_Dev [GWNUM 26.6]

Primality testing (38*10^91997-83)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number
Running N-1 test using base 5
Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 305613-bit number
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
(38*10^91997-83)/99 is Fermat and Lucas PRP! (4293.2813s+0.0028s)

```