Depression and Plateau Primes

(10^3-1) - 8*(10^2+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

(10^5-1) - 8*(10^4+1)

run"aprt-cle
Test number  N=? 19991

Preparatory test
    Pass !

 19991 is prime.
  0:00:00
OK

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

(10^9-1) - 8*(10^8+1)

run"aprt-cle
Test number  N=? 199999991

Preparatory test
    Pass !

 199999991 is prime.
  0:00:00
OK

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

*(10^41-1) - 8(10^40+1)**
== ID:B28650111EDE6 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 19999999999999999999999999999999999999991 Decimal size = 41 Binary size = 134 ----------------------------------------------------------------- 1) N-1 Test ----------------------------------------------------------------- N = Candidate S = 310 R = 64516129032258064516129032258064516129 B = 2 ----------------------------------------------------------------- 2) EC Test ----------------------------------------------------------------- N = R of preceding test S = 1705552 R = 37827125195982335631003119081491 A = 0 B = 16129032258064516129032258064516129118 T = 1 ----------------------------------------------------------------- 3) EC Test ----------------------------------------------------------------- N = R of preceding test S = 90840287 R = 416413536826257800668159 A =-3440 B =-77658 T = 3 ----------------------------------------------------------------- 4) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 65382 R = 6368932379343822469 B = 2 ----------------------------------------------------------------- 5) N+1 Test ----------------------------------------------------------------- N = R of preceding test S = 15470 R = 411695693558101 Q = 2 ----------------------------------------------------------------- 6) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 18900 R = 21782840929 B = 2 ----------------------------------------------------------------- 7) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/22/2003 04:59:12 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.

(10^41-1) - 8*(10^40+1)


== ID:B28650111EDE6 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 19999999999999999999999999999999999999991

Decimal size = 41
Binary size = 134

-----------------------------------------------------------------
1) N-1 Test
-----------------------------------------------------------------
N = Candidate
S = 310
R = 64516129032258064516129032258064516129
B = 2

-----------------------------------------------------------------
2) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 1705552
R = 37827125195982335631003119081491
A = 0
B = 16129032258064516129032258064516129118
T = 1

-----------------------------------------------------------------
3) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 90840287
R = 416413536826257800668159
A =-3440
B =-77658
T = 3

-----------------------------------------------------------------
4) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 65382
R = 6368932379343822469
B = 2

-----------------------------------------------------------------
5) N+1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 15470
R = 411695693558101
Q = 2

-----------------------------------------------------------------
6) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 18900
R = 21782840929
B = 2

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

Started 01/22/2003 04:59:12 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.

(10^87-1) - 8*(10^86+1)

== ID:B28690080FD5E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 199999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999991

Decimal size = 87
Binary size = 287


Started 01/26/2003 02:20:53 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.

(10^201-1) - 8*(10^200+1)

== ID:B28690438FB90 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 199999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999991

Decimal size = 201
Binary size = 666


Started 01/26/2003 07:40:43 PM
Running time 9s

Candidate certified prime

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

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

(10^731-1) - 8*(10^730+1)

[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286E037F40F6
Created=01/31/2003 04:17:51 PM
TestCount=110
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\pdp191_731.in
Expression=(10^731-1) - 8*(10^(729+1)+1)
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
HexadecimalSize=607
DecimalSize=731
BinarySize=2427

[Running Times]
Initialization=1.50s
1stPhase=19mn 28s
2ndPhase=3mn 4s
Total=22mn 33s


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

(10^1461-1) - 8*(10^1460+1)

[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B2907035FD5A9
Created=07/03/2003 03:43:35 PM
TestCount=214
Status=Candidate certified prime

[Running Times]
Initialization=2.99s
1stPhase=7h 46mn 55s
2ndPhase=50mn 22s
Total=8h 37mn 20s

[Candidate]
File=C:\Primo IN & OUT files\PDP1461.in
Expression=(10^1461-1)-8*(10^1460+1)
N$=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
HexadecimalSize=1213
DecimalSize=1461
BinarySize=4852

Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B2907035FD5A9-01.out available by
simple email request (244 KB).

(10^23673-1) - 8*(10^23672+1)

PRP to base 3,5,7.
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

(10^28631-1) - 8*(10^28630+1)

PRP to base 3,5,7.
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

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Patrick De Geest - Belgium

- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com