(10^3-1)/9 + 8*10^1
```*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(19*10^3-91)/99
N=191
*** N is prime!
Time: 0 sec
```

(10^9-1)/9 + 8*10^4
```== ID:B2814046DE224 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111191111

Decimal size = 9
Binary size = 27

-----------------------------------------------------------------
1) SPP Test
-----------------------------------------------------------------
N = Candidate

Started 11/02/2002 08:38:30 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.
```

(10^53-1)/9 + 8*10^26
```== ID:B2814046CACF6 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 11111111111111111111111111911111111111111111111111111

Decimal size = 53
Binary size = 173

Started 11/02/2002 08:37:11 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.
```

(10^375-1)/9 + 8*10^187
```== ID:B2814041168D2 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111191111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111

Decimal size = 375
Binary size = 1243

Started 11/02/2002 06:57:29 PM
Running time 1mn 41s

Candidate certified prime

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

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

(10^453-1)/9 + 8*10^226
```== ID:B280B00BAF28E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111191111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111

Decimal size = 453
Binary size = 1502

Started 10/24/2002 03:24:11 AM
Running time 4mn 14s

Candidate certified prime

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

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

(10^1749-1)/9 + 8*10^874
```[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3 - (1)874 9 (1)874
Format=2
ID=B27F5003D3A92
Created=10/02/2002 01:06:52 AM
TestCount=264
Status=Candidate certified prime

[Running Times]
Initialization=6.86s
1stPhase=12h 11mn 10s
2ndPhase=1h 2mn 44s
Total=13h 14mn 1s

Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen
using a 1.33 GHz Athlon chip.
The file "Primo-B27F5003D3A92-001.out" is 514 KB
and is available on demand by simple email request.
```

(10^26619-1)/9 + 8*10^13309
```C:\pfgw>pfgw64 -q"(10^26619-1)/9 + 8*10^13309"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

(10^26619-1)/9 + 8*10^13309 is 3-PRP! (3.8213s+0.0030s)
```

```

```