```

5*(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=(35*10^3-53)/99
N=353
*** N is prime!
Time: 0 sec

5*(10^9-1)/9 - 2*(10^8+1)

run"aprt-cle
Test number  N=? 355555553

Preparatory test
Pass !

355555553 is prime.
0:00:00
OK

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

5*(10^141-1)/9 - 2*(10^140+1)

== ID:B28690376117A =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 355555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555553

Decimal size = 141
Binary size = 467

Started 01/26/2003 04:07:49 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.

5*(10^231-1)/9 - 2*(10^230+1)

== ID:B286A000468C0 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 355555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555553

Decimal size = 231
Binary size = 766

Started 01/27/2003 12:04:48 AM
Running time 16s

Candidate certified prime

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

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

5*(10^427-1)/9 - 2*(10^426+1)

[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286B0165464E
Created=01/28/2003 06:30:14 AM
TestCount=74
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\pwp353_427.in
Expression=5*(10^427-1)/9 - 2*(10^(425+1)+1)
DecimalSize=427
BinarySize=1417

[Running Times]
Initialization=0.36s
1stPhase=1mn 38s
2ndPhase=28.50s
Total=2mn 7s

Proved prime with 'Primo 2.0.0 - beta 3'
by Patrick De Geest using a Pentium III 650 MHz chip.

5*(10^463-1)/9 - 2*(10^462+1)

== ID:B286C01100300 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 355555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
5555555555555555555555555555555555555555553

Decimal size = 463
Binary size = 1537

Started 01/29/2003 04:57:06 AM
Running time 6mn 52s

Candidate certified prime

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

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

5*(10^727-1)/9 - 2*(10^726+1)

[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286E00DB01D2
Created=01/31/2003 03:59:12 AM
TestCount=129
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\pdp353_727.in
Expression=5*(10^727-1)/9 - 2*(10^(725+1)+1)
DecimalSize=727
BinarySize=2414

[Running Times]
Initialization=1.73s
1stPhase=2h 10mn 2s
2ndPhase=10mn 9s
Total=2h 20mn 14s

Proved prime with 'Primo 2.0.0 - beta 3'
by Patrick De Geest using a Pentium III 650 MHz chip.

5*(10^1975-1)/9 - 2*(10^1974+1)

32*(10^1974-1)9+1
was the largest proven plateau prime known in May 2001. In base 10,
it consists of 1973 successive 5's sandwiched by a pair of 3's.

C:\Pdp>pfgw -hhd1974.fac -l -tm -q"32*(10^1974-1)/9+1"
PFGW Version 1.1 for Windows

Output logging to file pfgw.out
Primality testing 32*(10^1974-1)/9+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file hd1974.fac
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 33.36%
32*(10^1974-1)/9+1 is prime! (6.430000 seconds)

Helper file and proof by David Broadhurst.
Timing : reproduced on a Pentium III 650 MHz chip.

Compare the timings with this newly created Primo Certificate !

[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B290D009E7A50
Created=07/09/2003 02:53:12 AM
TestCount=274
Status=Candidate certified prime

[Running Times]
Initialization=6.51s
1stPhase=21h 5mn 58s
2ndPhase=2h 7mn 17s
Total=23h 13mn 22s

[Candidate]
File=C:\Primo IN & OUT files\PDP1975.in
Expression=5*(10^1975-1)/9-2*(10^1974+1)
DecimalSize=1975
BinarySize=6560

Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B290D009E7A50-01.out available by
simple email request (414 KB).

5*(10^7231-1)/9 - 2*(10^7230+1)

3-PRP!

5*(10^45861-1)/9 - 2*(10^45860+1)

3-PRP!
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].

5*(10^47305-1)/9 - 2*(10^47304+1)

3-PRP!
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].

```