(10^7-1)/9 + 6*10^3
```== ID:B281304A5E58E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 1117111

Decimal size = 7
Binary size = 21

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

Started 11/01/2002 09:39:41 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.
```

(10^67-1)/9 + 6*10^33
```== ID:B281304A47BCC =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111111111111111111111111111111711111111111111111111111111\
1111111

Decimal size = 67
Binary size = 220

Started 11/01/2002 09:38:08 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.
```

(10^623-1)/9 + 6*10^311
```== ID:B280A00988F6E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111117111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111

Decimal size = 623
Binary size = 2067

Started 10/23/2002 02:46:38 AM
Running time 18mn 15s

Candidate certified prime

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

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

(10^5867-1)/9 + 6*10^2933
```
[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B28500468C258
Created=01/01/2003 08:32:54 PM
TestCount=857
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\Work\Arnault.in
Expression=(10^5867-1)/9 + 6*10^2933
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
HexadecimalSize=4872
DecimalSize=5867
BinarySize=19487

[Running Times]
Initialization=1mn 57s
1stPhase=3260h 10mn 40s
2ndPhase=145h 33mn 20s
Total=3405h 45mn 57s

[Backtrack Report]
File=C:\Program Files\Primo200\Work\Primo-B28500468C258-001.br

Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen
using a 1.33 GHz Athlon chip.
To download the certificate: ecpp5867.zip (3390 KB)
```

(10^44471-1)/9 + 6*10^22235
```C:\pfgw>pfgw64 -q"(10^44471-1)/9+6*10^22235"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

(10^44471-1)/9+6*10^22235 is 3-PRP! (25.6771s+0.0039s)
```

(10^78331-1)/9 + 6*10^39165
```C:\pfgw>pfgw64 -q"(10^78331-1)/9+6*10^39165"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

(10^78331-1)/9+6*10^39165 is 3-PRP! (83.9023s+0.0023s)
```

(10^83171-1)/9 + 6*10^41585
```C:\pfgw>pfgw64 -q"(10^83171-1)/9+6*10^41585"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

(10^83171-1)/9+6*10^41585 is 3-PRP! (96.0888s+0.0062s)
```

```

```

( © All rights reserved ) - Last modified : March 25, 2023.

Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com