(10^3-1)/9 + 2*(10^2+1)
```*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(31*10^3-13)/99
N=313
*** N is prime!
Time: 0 sec
```

(10^13-1)/9 + 2*(10^12+1)
```run"aprt-cle
Test number  N=? (10^13-1)\9 + 2*(10^12+1)

Preparatory test
Pass !

Main test  for P= 2
for Q= 3    for Q= 5    for Q= 7    for Q= 13    for Q= 11

Main test  for P= 3
for Q= 7    for Q= 13

Main test  for P= 5
for Q= 11     Pass !

3111111111113 is prime.
0:00:00
OK

Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.
```

(10^15-1)/9 + 2*(10^14+1)
```== ID:B286400B892F0 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 311111111111113

Decimal size = 15
Binary size = 49

-----------------------------------------------------------------
1) N+1 Test
-----------------------------------------------------------------
N = Candidate
S = 46282
R = 6722075777
Q = 14

-----------------------------------------------------------------
2) SPP Test
-----------------------------------------------------------------
N = R of preceding test

Started 01/21/2003 03:21:36 AM
Running time < 1s

Candidate certified prime

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

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

(10^31-1)/9 + 2*(10^30+1)
```
== ID:B286500FF6130 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 3111111111111111111111111111113

Decimal size = 31
Binary size = 102

-----------------------------------------------------------------
1) N+1 Test
-----------------------------------------------------------------
N = Candidate
S = 1314
R = 2367664468121089125655335701
Q = 7

-----------------------------------------------------------------
2) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 2016936692500
R = 1173891315937271
A =-140
B = 784
T = 0

-----------------------------------------------------------------
3) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 356090
R = 3296614103
B = 2

-----------------------------------------------------------------
4) SPP Test
-----------------------------------------------------------------
N = R of preceding test

Started 01/22/2003 04:38:56 AM
Running time < 1s

Candidate certified prime

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

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

(10^105-1)/9 + 2*(10^104+1)
```== ID:B2869034BB06A =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 311111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111113

Decimal size = 105
Binary size = 348

Started 01/26/2003 03:21:32 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.
```

(10^127-1)/9 + 2*(10^126+1)
```== ID:B286903704C7C =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 311111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
1111113

Decimal size = 127
Binary size = 421

Started 01/26/2003 04:01:31 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.
```

(10^343-1)/9 + 2*(10^342+1)
```== ID:B286A0024994C =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 311111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
1111111111111111111111111111111111111111113

Decimal size = 343
Binary size = 1138

Started 01/27/2003 12:39:58 AM
Running time 2mn 49s

Candidate certified prime

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

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

(10^601-1)/9 + 2*(10^600+1)
```== ID:B286D0122DBA6 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 311111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
3

Decimal size = 601
Binary size = 1995

Started 01/30/2003 05:17:41 AM
Running time 27mn 45s

Candidate certified prime

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

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

(10^9825-1)/9 + 2*(10^9824+1)
```3-PRP!

```

```

```