Depression and Plateau Primes

8*(10^3-1)/9 - (10^2+1)

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(78*10^3-87)/99
N=787
*** N is prime!
Time: 0 sec

8*(10^5-1)/9 - (10^4+1)

run"aprt-cle
Test number  N=? 78887

Preparatory test
    Pass !

 78887 is prime.
  0:00:00
OK

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

8*(10^87-1)/9 - (10^86+1)

== ID:B28690085E1B6 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 788888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888887

Decimal size = 87
Binary size = 289


Started 01/26/2003 02:26:14 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.

8*(10^113-1)/9 - (10^112+1)

== ID:B28690351CC48 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 788888888888888888888888888888888888888888888888888888888888\
    88888888888888888888888888888888888888888888888888887

Decimal size = 113
Binary size = 376


Started 01/26/2003 03:28:12 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.

8*(10^171-1)/9 - (10^170+1)

== ID:B286904009F20 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 788888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888887

Decimal size = 171
Binary size = 568


Started 01/26/2003 06:39:09 PM
Running time 5s

Candidate certified prime

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

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

8*(10^567-1)/9 - (10^566+1)

== ID:B286C03C47DCE =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 788888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888887

Decimal size = 567
Binary size = 1884


Started 01/29/2003 05:33:28 PM
Running time 12mn 28s

Candidate certified prime

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

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

8*(10^1689-1)/9 - (10^1688+1)

[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B290B00657C49
Created=07/07/2003 01:50:55 AM
TestCount=259
Status=Candidate certified prime

[Running Times]
Initialization=4.46s
1stPhase=11h 10mn 1s
2ndPhase=1h 25mn 43s
Total=12h 35mn 48s

[Candidate]
File=C:\Primo IN & OUT files\PDP1689.in
Expression=8*(10^1689-1)/9-(10^1688+1)
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
HexadecimalSize=1403
DecimalSize=1689
BinarySize=5611

Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B290B00657C49-01.out available by
simple email request (332 KB).

8*(10^8903-1)/9 - (10^8902+1)

3-PRP!

8*(10^115811-1)/9 - (10^115810+1)

Tested by Ray Chandler


PFGW Version 3.4.8.64BIT.20110617.Win_Dev [GWNUM 26.6] 
 
Primality testing (71*10^115810-17)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge] 
Running N-1 test using base 5 
Generic modular reduction using generic reduction Core2 type-1 FFT length 48K, Pass1=64, Pass2=768 on A 384719-bit number 
Running N-1 test using base 7 
Generic modular reduction using generic reduction Core2 type-1 FFT length 48K, Pass1=64, Pass2=768 on A 384719-bit number 
Running N+1 test using discriminant 17, base 1+sqrt(17) 
Generic modular reduction using generic reduction Core2 type-1 FFT length 48K, Pass1=64, Pass2=768 on A 384719-bit number 
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof) 
(71*10^115810-17)/9 is Fermat and Lucas PRP! (5003.3912s+0.0088s)

8*(10^165717-1)/9 - (10^165716+1)

By Serge Batalov dd. January 19, 2023.

PRP Source : https://stdkmd.net/nrr/7/78887.htm#prime

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Patrick De Geest - Belgium

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