Depression and Plateau Primes

7*(10^7-1)/9 - 6*(10^6+1)

run"aprt-cle
Test number  N=? 1777771

Preparatory test
    Pass !

 1777771 is prime.
  0:00:00
OK

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

*7(10^49-1)/9 - 6(10^48+1)*
== ID:B286501165296 ============================================= PRIMO 1.2.1 - Primality Certificate ----------------------------------------------------------------- Candidate ----------------------------------------------------------------- N = 1777777777777777777777777777777777777777777777771 Decimal size = 49 Binary size = 161 ----------------------------------------------------------------- 1) EC Test ----------------------------------------------------------------- N = Candidate S = 667203784048 R = 2664519926718342504627184075295192647 A =-35 B = 98 T = 1 ----------------------------------------------------------------- 2) EC Test ----------------------------------------------------------------- N = R of preceding test S = 300684 R = 8861528803389413816240533028047 A = 0 B = 8 T = 1 ----------------------------------------------------------------- 3) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 6 R = 1476921467231568969373422171341 B = 2 ----------------------------------------------------------------- 4) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 691578749020 R = 2135579598598766917 B = 2 ----------------------------------------------------------------- 5) N-1 Test ----------------------------------------------------------------- N = R of preceding test S = 774475644 R = 2757452239 B = 2 ----------------------------------------------------------------- 6) SPP Test ----------------------------------------------------------------- N = R of preceding test Started 01/22/2003 05:04:00 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.

7*(10^49-1)/9 - 6*(10^48+1)



== ID:B286501165296 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 1777777777777777777777777777777777777777777777771

Decimal size = 49
Binary size = 161

-----------------------------------------------------------------
1) EC Test
-----------------------------------------------------------------
N = Candidate
S = 667203784048
R = 2664519926718342504627184075295192647
A =-35
B = 98
T = 1

-----------------------------------------------------------------
2) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 300684
R = 8861528803389413816240533028047
A = 0
B = 8
T = 1

-----------------------------------------------------------------
3) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 6
R = 1476921467231568969373422171341
B = 2

-----------------------------------------------------------------
4) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 691578749020
R = 2135579598598766917
B = 2

-----------------------------------------------------------------
5) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 774475644
R = 2757452239
B = 2

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

Started 01/22/2003 05:04:00 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.

7*(10^103-1)/9 - 6*(10^102+1)

== ID:B286903492426 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 177777777777777777777777777777777777777777777777777777777777\
    7777777777777777777777777777777777777777771

Decimal size = 103
Binary size = 340


Started 01/26/2003 03:18:45 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.

7*(10^193-1)/9 - 6*(10^192+1)

== ID:B2869040322FE =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 177777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    7777777777771

Decimal size = 193
Binary size = 639


Started 01/26/2003 06:41:54 PM
Running time 7s

Candidate certified prime

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

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

7*(10^367-1)/9 - 6*(10^366+1)

== ID:B286A011D9C54 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 177777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    7777771

Decimal size = 367
Binary size = 1217


Started 01/27/2003 05:11:57 AM
Running time 4mn 51s

Candidate certified prime

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

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

7*(10^1003-1)/9 - 6*(10^1002+1)


[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286603C0C4FE
Created=01/23/2003 05:29:24 PM
TestCount=148
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\d1003.in
Expression=16*(10^1002-1)/9-5
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
HexadecimalSize=833
DecimalSize=1003
BinarySize=3330

[Running Times]
Initialization=1.38s
1stPhase=1h 26mn 31s
2ndPhase=10mn 12s
Total=1h 36mn 45s

[Backtrack Report]
File=C:\Program Files\Primo200\Primo-B286603C0C4FE-001.br


Proved prime with 'Primo 2.0.0 - beta 3' by David Broadhurst.
The Primo certificate of the above PDP (the file is 148 KB)
is available on demand by simple email request.

7*(10^20365-1)/9 - 6*(10^20364+1)

3-PRP!
PFGW Version 20040816.Win_Stable (v1.2 RC1a) [FFT v23.8]

7*(10^37447-1)/9 - 6*(10^37446+1)

3-PRP!
PFGW Version 20040816.Win_Stable (v1.2 RC1a) [FFT v23.8]

7*(10^56083-1)/9 - 6*(10^56082+1)

By Serge Batalov dd. May 17, 2009.

(16*10^56082-61)/9 is 3-PRP! (199.1310s+0.0043s)

Using the -tc switch
PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing (16*10^56082-61)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
(16*10^56082-61)/9 is Fermat and Lucas PRP! (1087.4648s+0.0122s)

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Patrick De Geest - Belgium

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