Depression and Plateau Primes

8*(10^3-1)/9 - 5*(10^2+1)

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(38*10^3-83)/99
N=383
*** N is prime!
Time: 0 sec

8*(10^13-1)/9 - 5*(10^12+1)

run"aprt-cle
Test number  N=? 8*(10^13-1)\9 - 5*(10^12+1)

Preparatory test
    Pass !

Main test  for P= 2
   for Q= 3    for Q= 5    for Q= 7    for Q= 13    for Q= 11

Main test  for P= 3
   for Q= 7    for Q= 13

Main test  for P= 5
   for Q= 11     Pass !

 3888888888883 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(10^31-1)/9 - 5(10^30+1)*
== ID:B286501018F78 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 3888888888888888888888888888883 Decimal size = 31 Binary size = 102 ----------------------------------------------------------------- 1) EC Test ----------------------------------------------------------------- N = Candidate S = 39686931 R = 97989156402365597673589 A = 0 B = 16 T = 2 ----------------------------------------------------------------- 2) N+1 Test ----------------------------------------------------------------- N = R of preceding test S = 9885590 R = 9912322522213201 Q = 2 ----------------------------------------------------------------- 3) EC Test ----------------------------------------------------------------- N = R of preceding test S = 74775652 R = 132560833 A = 0 B = 19 T = 1 ----------------------------------------------------------------- 4) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/22/2003 04:41:19 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*(10^31-1)/9 - 5*(10^30+1)


== ID:B286501018F78 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 3888888888888888888888888888883

Decimal size = 31
Binary size = 102

-----------------------------------------------------------------
1) EC Test
-----------------------------------------------------------------
N = Candidate
S = 39686931
R = 97989156402365597673589
A = 0
B = 16
T = 2

-----------------------------------------------------------------
2) N+1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 9885590
R = 9912322522213201
Q = 2

-----------------------------------------------------------------
3) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 74775652
R = 132560833
A = 0
B = 19
T = 1

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

Started 01/22/2003 04:41:19 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*(10^61-1)/9 - 5*(10^60+1)

== ID:B28680499236C =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 388888888888888888888888888888888888888888888888888888888888\
    3

Decimal size = 61
Binary size = 202


Started 01/25/2003 09:25:44 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*(10^117-1)/9 - 5*(10^116+1)

== ID:B286903693A86 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 388888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888883

Decimal size = 117
Binary size = 388


Started 01/26/2003 03:53:47 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*(10^291-1)/9 - 5*(10^290+1)

== ID:B286A001A6AB2 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 388888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888883

Decimal size = 291
Binary size = 966


Started 01/27/2003 12:28:51 AM
Running time 1mn 34s

Candidate certified prime

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

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

8*(10^633-1)/9 - 5*(10^632+1)

== ID:B286D01403F8E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 388888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888883

Decimal size = 633
Binary size = 2102


Started 01/30/2003 05:49:47 AM
Running time 52mn 3s

Candidate certified prime

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

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

8*(10^1065-1)/9 - 5*(10^1064+1)

[PRIMO - Primality Certificate]
Version=2.2.0 beta 1
WebSite=http://www.ellipsa.net/
Format=3
ID=B29570501FA18
Created=09/21/2003 11:20:17 PM
TestCount=159
Status=Candidate certified prime

[Running Times]
Initialization=2.20s
1stPhase=47mn 38s
2ndPhase=10mn 10s
Total=57mn 51s

[Candidate]
File=C:\Primo IN & OUT files\PDP1065.in
Expression=8*(10^1065-1)/9-5*(10^1064+1)
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
HexadecimalSize=885
DecimalSize=1065
BinarySize=3537


Proved prime with 'Primo 2.2.0 - beta 1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B29570501FA18-01.out available by
simple email request (121 KB).

8*(10^1495-1)/9 - 5*(10^1494+1)

[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B290900F01444
Created=07/05/2003 04:22:19 AM
TestCount=238
Status=Candidate certified prime

[Running Times]
Initialization=5.35s
1stPhase=8h 19mn 11s
2ndPhase=36mn 51s
Total=8h 56mn 8s

[Candidate]
File=C:\Primo IN & OUT files\PDP1495.in
Expression=8*(10^1495-1)/9-5*(10^1494+1)
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
HexadecimalSize=1242
DecimalSize=1495
BinarySize=4965


Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B290900F01444-01.out available by
simple email request (284 KB).

8*(10^5433-1)/9 - 5*(10^5432+1)

Xinyao Chen informs me (May 19,2022) that this number is
now a proven plateau-and-depression prime.
Proof was done by Maksym Voznyy on May 16, 2016.

See source at
https://stdkmd.net/nrr/records.htm#pdprime

8*(10^7363-1)/9 - 5*(10^7362+1)

Xinyao Chen informs me (May 19,2022) that this number is
now a proven plateau-and-depression prime.
Proof was done by Maksym Voznyy on December 8, 2020.

See source at
https://stdkmd.net/nrr/records.htm#pdprime

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Patrick De Geest - Belgium

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