Depression and Plateau Primes

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

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(79*10^3-97)/99
N=797
*** N is prime!
Time: 0 sec

(10^5-1) - 2*(10^4+1)

run"aprt-cle
Test number  N=? 79997

Preparatory test
    Pass !

 79997 is prime.
  0:00:00
OK

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

(10^29-1) - 2*(10^28+1)

== ID:B286500FBC5C0 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 79999999999999999999999999997

Decimal size = 29
Binary size = 97

-----------------------------------------------------------------
1) EC Test
-----------------------------------------------------------------
N = Candidate
S = 3464624968
R = 23090522275540976917
A =-1
B = 0
T = 2

-----------------------------------------------------------------
2) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 1324356
R = 17435283470261
B = 2

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

Started 01/22/2003 04:35:00 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.

(10^157-1) - 2*(10^156+1)

== ID:B286903FBD06C =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 799999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    9999999999999999999999999999999999997

Decimal size = 157
Binary size = 522


Started 01/26/2003 06:33:54 PM
Running time 3s

Candidate certified prime

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

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

(10^323-1) - 2*(10^322+1)

== ID:B286A001F9AFA =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 799999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    99999999999999999999997

Decimal size = 323
Binary size = 1073


Started 01/27/2003 12:34:31 AM
Running time 2mn 6s

Candidate certified prime

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

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

(10^353-1) - 2*(10^352+1)

== ID:B286A002E5284 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 799999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    99999999999999999999999999999999999999999999999999997

Decimal size = 353
Binary size = 1173


Started 01/27/2003 12:50:35 AM
Running time 1mn 39s

Candidate certified prime

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

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

(10^1213-1) - 2*(10^1212+1)

[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B290400B122EC
Created=06/30/2003 03:13:30 AM
TestCount=185
Status=Candidate certified prime

[Running Times]
Initialization=1.76s
1stPhase=1h 59mn 38s
2ndPhase=12mn 4s
Total=2h 11mn 45s

[Candidate]
File=C:\Primo IN files\PDP1213.in
Expression=(10^1213-1)-2*(10^1212+1)
N$=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
HexadecimalSize=1008
DecimalSize=1213
BinarySize=4030

Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B290400B122EC-01.out available by
simple email request (175 KB).

(10^1285-1) - 2*(10^1284+1)

[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B290700E3E1F3
Created=07/03/2003 04:08:58 AM
TestCount=186
Status=Candidate certified prime

[Running Times]
Initialization=3.65s
1stPhase=3h 14mn 31s
2ndPhase=15mn 6s
Total=3h 29mn 41s

[Candidate]
File=C:\Primo IN & OUT files\PDP1285.in
Expression=(10^1285-1)-2*(10^1284+1)
N$=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
HexadecimalSize=1068
DecimalSize=1285
BinarySize=4269

Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B290700E3E1F3-01.out available by
simple email request (182 KB).

(10^7985-1) - 2*(10^7984+1)

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 8*10^7984-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Running N+1 test using discriminant 5, base 6+sqrt(5)
Running N+1 test using discriminant 5, base 9+sqrt(5)
Running N+1 test using discriminant 5, base 11+sqrt(5)
Calling N+1 BLS with factored part 0.26% and helper 0.02% (0.81% proof)
8*10^7984-3 is Fermat and Lucas PRP! (47.7224s+0.0009s)

(10^15193-1) - 2*(10^15192+1)

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 8*10^15192-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Running N+1 test using discriminant 5, base 6+sqrt(5)
Calling N+1 BLS with factored part 0.09% and helper 0.04% (0.31% proof)
8*10^15192-3 is Fermat and Lucas PRP! (110.5068s+0.0009s)

(10^84773-1) - 2*(10^84772+1)

By Ray Chandler

PFGW Version 3.4.4.64BIT.20101104.Win_Dev [GWNUM 26.4] 
 
Primality testing (72*10^84772-27)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] 
Running N-1 test using base 2 
Running N+1 test using discriminant 5, base 5+sqrt(5) 
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.07% proof) 
(72*10^84772-27)/9 is Fermat and Lucas PRP! (2445.9553s+0.0023s)

(10^119931-1) - 2*(10^119930+1)

By Ray Chandler

PFGW Version 3.4.6.64BIT.20110307.Win_Dev [GWNUM 26.5] 
 
Primality testing 8*10^119930-3 [N-1/N+1, Brillhart-Lehmer-Selfridge] 
Running N-1 test using base 2 
Running N+1 test using discriminant 5, base 5+sqrt(5) 
Calling N+1 BLS with factored part 0.00% and helper 0.00% (0.01% proof) 
8*10^119930-3 is Fermat and Lucas PRP! (1506.0321s+0.0031s)

(10^148861-1) - 2*(10^148860+1)

By Ray Chandler (srsieve,PFGW)

PFGW Version 3.4.6.64BIT.20110307.Win_Dev [GWNUM 26.5]

Primality testing 8*10^148860-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N+1 BLS with factored part 0.00% and helper 0.00% (0.02% proof)
8*10^148860-3 is Fermat and Lucas PRP! (2120.6055s+0.0046s)

(10^219741-1) - 2*(10^219740+1)

By Serge Batalov dd. January 14, 2023.

PRP Source : https://stdkmd.net/nrr/7/79997.htm#prime

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Patrick De Geest - Belgium

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