(78*10^3-87)/99
```*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(78*10^3-87)/99
N=787
*** N is prime!
Time: 0 sec
```

(78*10^5-87)/99
```*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(78*10^5-87)/99
N=78787
*** N is prime!
Time: 0 sec
```

(78*10^21-87)/99
```
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(78*10^21-87)/99
N=787878787878787878787
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3 divides N - 1
Factor: 653 divides N - 1
Factor: 967 divides N - 1
Factorization results: F1=0.3148 F2=0.0288
F1=3788706
F2=4
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=87878787878787878785
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=72261441967267298276
Pass: gcd(3^((N-1)/653) - 1, N) = 1: R20=32332421815511943304
Pass: gcd(3^((N-1)/967) - 1, N) = 1: R20=89479634850406340140
BLS tests passed: F1=0.3148 F2=0.0288
APRCL test
T=12
S=35
APRCL main test (1) at level 1 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=87878787878787878786
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=83636363636363636363
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL tests for p=2 completed
APRCL main test (2) at level 1 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=1
APRCL tests for p=3 completed
Main divisor test: F1=0.3004 F2=0.0288 G=0.4031 S=0.0739 T=12
G=265209420
Main divisor test passed: 12/12
Final divisor test: F=0.3148 G=0.4031 H=1.0327 t=-1 a=1
Final divisor test passed: 3/3 r=3 i=0
*** N is prime!
Time: 0 sec
```

(78*10^27-87)/99
```
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(78*10^27-87)/99
N=787878787878787878787878787
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3 divides N - 1
Factor: 7307 divides N + 1
Factorization results: F1=0.0289 F2=0.1660
F1=6
F2=29228
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=87878787878787878785
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=98572212658718603580
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=65480855587662710716
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/7307}, N) = 1: d=5 p=1 q=-1 R20=41108120264446100386
BLS tests passed: F1=0.0289 F2=0.1660
APRCL test
T=180
S=899123225
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=1 R20=87878787878787878786
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=63636363636363636363
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=1 R20=5594405594405594405
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=87878787878787878786
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=3 R20=92696652089288477356
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=87878787878787878786
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=1
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=87878787878787878784
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=2 R20=87878787878787878784
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=87878787878787878784
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=3 R20=16614364406731958847
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=2 R20=92587027297771099424
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=79484753886418818781
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=4 R20=81796193594097383401
APRCL tests for p=5 completed
Main divisor test: F1=0.0177 F2=0.1660 G=0.5167 S=0.3329 T=180
G=78838720860900
Main divisor test passed: 60/180
*** N is prime!
Time: 0 sec
```

(78*10^95-87)/99
```
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(78*10^95-87)/99
N=78787878787878787878787878787878787878787878787878787878787878787878787878787878787878787878787
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3^4 divides N - 1
Factor: 23 divides N + 1
Factor: 3467 divides N - 1
Factor: 33091 divides N + 1
Factorization results: F1=0.0606 F2=0.0683
F1=561654
F2=3044372
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=87878787878787878785
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=57237901962179769224
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=84164504975974825615
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/23}, N) = 1: d=5 p=1 q=-1 R20=24861110972262906010
Pass: gcd(5^((N-1)/3467) - 1, N) = 1: R20=41161634633370851157
Pass: gcd(U{(N+1)/33091}, N) = 1: d=5 p=1 q=-1 R20=89543500525101488061
BLS tests passed: F1=0.0606 F2=0.0683
APRCL test
T=2520
S=56325605729274370962234592119010146425
APRCL main test (1) at level 5 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=87878787878787878786
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=63636363636363636363
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=87878787878787878786
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=1864801864801864801
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=87878787878787878786
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=87878787878787878786
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=0 R20=21903528702776216885
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=3 R20=95092635633176173716
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=20638915636015846632
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=0 R20=26977263719237559903
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=0 R20=1
APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=0 R20=1
APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=87878787878787878786
APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=87878787878787878786
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=1 R20=24929846418666725480
APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=1 R20=87878787878787878786
APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=7 R20=2994249454689668847
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=5 R20=60533274194373837834
APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=5 R20=60244585646999496874
APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=0 R20=83149324215648330686
APRCL tests for p=2 completed
APRCL main test (2) at level 5 for p=3
APRCL L_3 condition satisfied
APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=2 R20=87878787878787878784
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=87878787878787878784
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=87878787878787878784
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=2 R20=0
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=6 R20=87878787878787878780
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=2 R20=0
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=1
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=5 R20=0
APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=1 R20=1
APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=1 R20=1
APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=0 R20=6
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=6 R20=87878787878787878780
APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=7 R20=0
APRCL tests for p=3 completed
APRCL main test (3) at level 5 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=53668920611069371399
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=75048087535080251001
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=85691366771721515070
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=87713957745397567136
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=3 R20=41691463333994577795
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=2 R20=63000640487669080917
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=1 R20=84218286589069872847
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=0 R20=37009210451109582365
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=1 R20=43583364880211995024
APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=0 R20=36221525547901860258
APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=0 R20=26042391364844991587
APRCL tests for p=5 completed
APRCL main test (4) at level 5 for p=7
APRCL L_7 condition satisfied
APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=3 R20=88916016535025104462
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=0 R20=10653111923440322197
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=1 R20=89356521085358701414
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=4 R20=8377145792707238003
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=5 R20=69399618463530046444
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=0 R20=27353185954799300858
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=4 R20=1640995420112024389
APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=6 R20=27804052396759792604
APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=4 R20=328729913926784646
APRCL tests for p=7 completed
Main divisor test: F1=0.0574 F2=0.0683 G=0.5235 S=0.3978 T=2520
G=48155117882458148604063672031073992673053652672700
Main divisor test passed: 2520/2520
*** N is prime!
Time: 1 sec
```

(78*10^2075-87)/99
```== BPI:B263C01D19308 ============================================

TITANIX 2.1.0 - Primality Certificate

Started 07.18.2001 at 08:28:31 AM
Running time 65h 13mn 12s

Candidate certified prime

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

Proved prime with Titanix by Hans Rosenthal.
The zipped file "787_1037.zip" is 395 KB.
When unpacked the file "Titanix-B263C01D19308-001.out" is 919 KB
and is available on demand by simple email request.
```

(78*10^2165-87)/99
```== ID:B264E0446A380 =============================================

PRIMO 0.1.0 - Primality Certificate

Started 08.05.2001 07:55:38 PM
Running time 56h 49mn 43s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "787_1082.zip" is 477 KB.
When unpacked the file "Primo-B264E0446A380-001.out" is 1104 KB
and is available on demand by simple email request.
```

(78*10^3047-87)/99
```== ID:B266C0038C520 =============================================

PRIMO 0.1.0 - Primality Certificate

Started 09.04.2001 01:02:00 AM
Running time 179h 6mn 23s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "787_1523.zip" is 909 KB.
When unpacked the file "Primo-B266C0038C520-001.out" is 2079 KB
and is available on demand by simple email request.
```

(78*10^3503-87)/99
```== ID:B269801BB6D76 =============================================

PRIMO 1.1.0 - Primality Certificate

Started 11.24.2001 09:00:16 PM
Running time 420h 1mn 1s
Started 12.10.2001 01:54:33 AM
Running time 44h 15mn 33s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "787_1751.zip" is 1150 KB.
When unpacked the file "Primo-B269801BB6D76.out" is 2644 KB
and is available on demand by simple email request.
```

(78*10^16791-87)/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

(78*10^16791-87)/99 is 3-PRP! (75.680000 seconds)
(78*10^16791-87)/99 is 5-PRP! (77.780000 seconds)
(78*10^16791-87)/99 is 7-PRP! (75.910000 seconds)
(78*10^16791-87)/99 is 11-PRP! (75.690000 seconds)
(78*10^16791-87)/99 is 13-PRP! (75.800000 seconds)
(78*10^16791-87)/99 is 17-PRP! (75.910000 seconds)
(78*10^16791-87)/99 is 19-PRP! (78.210000 seconds)
(78*10^16791-87)/99 is 23-PRP! (75.800000 seconds)
(78*10^16791-87)/99 is 29-PRP! (76.290000 seconds)
(78*10^16791-87)/99 is 31-PRP! (76.460000 seconds)
(78*10^16791-87)/99 is 37-PRP! (75.690000 seconds)
(78*10^16791-87)/99 is 41-PRP! (83.980000 seconds)
(78*10^16791-87)/99 is 43-PRP! (75.850000 seconds)
(78*10^16791-87)/99 is 47-PRP! (75.850000 seconds)
(78*10^16791-87)/99 is 53-PRP! (75.850000 seconds)
(78*10^16791-87)/99 is 59-PRP! (78.870000 seconds)
(78*10^16791-87)/99 is 61-PRP! (75.850000 seconds)
(78*10^16791-87)/99 is 251-PRP! (77.880000 seconds)
```

(78*10^34883-87)/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

(78*10^34883-87)/99 is 3-PRP! (488.500000 seconds)
(78*10^34883-87)/99 is 5-PRP! (505.650000 seconds)
(78*10^34883-87)/99 is 7-PRP! (495.430000 seconds)
(78*10^34883-87)/99 is 11-PRP! (494.390000 seconds)
(78*10^34883-87)/99 is 13-PRP! (501.800000 seconds)
(78*10^34883-87)/99 is 17-PRP! (496.470000 seconds)
(78*10^34883-87)/99 is 19-PRP! (494.990000 seconds)
(78*10^34883-87)/99 is 23-PRP! (488.120000 seconds)
(78*10^34883-87)/99 is 29-PRP! (495.700000 seconds)
(78*10^34883-87)/99 is 31-PRP! (494.210000 seconds)
(78*10^34883-87)/99 is 37-PRP! (494.600000 seconds)
(78*10^34883-87)/99 is 41-PRP! (496.520000 seconds)
(78*10^34883-87)/99 is 43-PRP! (496.850000 seconds)
(78*10^34883-87)/99 is 47-PRP! (501.200000 seconds)
(78*10^34883-87)/99 is 53-PRP! (495.980000 seconds)
(78*10^34883-87)/99 is 59-PRP! (498.940000 seconds)
(78*10^34883-87)/99 is 61-PRP! (496.260000 seconds)
(78*10^34883-87)/99 is 67-PRP! (493.890000 seconds)
(78*10^34883-87)/99 is 71-PRP! (497.790000 seconds)
(78*10^34883-87)/99 is 73-PRP! (493.840000 seconds)
(78*10^34883-87)/99 is 79-PRP! (498.010000 seconds)
(78*10^34883-87)/99 is 83-PRP! (503.450000 seconds)
(78*10^34883-87)/99 is 89-PRP! (497.900000 seconds)
(78*10^34883-87)/99 is 97-PRP! (494.880000 seconds)
(78*10^34883-87)/99 is 101-PRP! (501.300000 seconds)
(78*10^34883-87)/99 is 103-PRP! (492.020000 seconds)
(78*10^34883-87)/99 is 107-PRP! (494.440000 seconds)
(78*10^34883-87)/99 is 109-PRP! (492.960000 seconds)
(78*10^34883-87)/99 is 113-PRP! (491.470000 seconds)
(78*10^34883-87)/99 is 127-PRP! (503.390000 seconds)
(78*10^34883-87)/99 is 251-PRP! (493.620000 seconds)
```

```

```