5*(10^3-1)/9 + 2*(10^2+1)
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(75*10^3-57)/99
N=757
*** N is prime!
Time: 0 sec

5*(10^5-1)/9 + 2*(10^4+1)
run"aprt-cle
Test number  N=? 75557

Preparatory test
Pass !

75557 is prime.
0:00:00
OK

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

5*(10^11-1)/9 + 2*(10^10+1)
run"aprt-cle
Test number  N=? 5*(10^11-1)\9 + 2*(10^10+1)

Preparatory test
Pass !

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

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

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

75555555557 is prime.
0:00:00
OK

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

5*(10^21-1)/9 + 2*(10^20+1)
== ID:B286400C6CC4E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 755555555555555555557

Decimal size = 21
Binary size = 70

-----------------------------------------------------------------
1) N-1 Test
-----------------------------------------------------------------
N = Candidate
S = 57204
R = 13208089566386189
B = 2

-----------------------------------------------------------------
2) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 1358276
R = 9724157363
B = 2

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

Started 01/21/2003 03:37:08 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.

5*(10^23-1)/9 + 2*(10^22+1)
== ID:B286400C8E222 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 75555555555555555555557

Decimal size = 23
Binary size = 76

-----------------------------------------------------------------
1) N-1 Test
-----------------------------------------------------------------
N = Candidate
S = 85436
R = 884352679848723671
B = 2

-----------------------------------------------------------------
2) N+1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 28296
R = 31253628776107
Q = 11

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

Started 01/21/2003 03:39:25 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.

5*(10^59-1)/9 + 2*(10^58+1)
== ID:B286804962CFC =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 75555555555555555555555555555555555555555555555555555555557

Decimal size = 59
Binary size = 196

Started 01/25/2003 09:22:30 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.

5*(10^75-1)/9 + 2*(10^74+1)
== ID:B28690076EB16 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 755555555555555555555555555555555555555555555555555555555555\
555555555555557

Decimal size = 75
Binary size = 249

Started 01/26/2003 02:09:53 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.

5*(10^83-1)/9 + 2*(10^82+1)

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 755555555555555555555555555555555555555555555555555555555555\
55555555555555555555557

Decimal size = 83
Binary size = 276

Started 01/26/2003 02:11:39 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.

5*(10^209-1)/9 + 2*(10^208+1)
== ID:B286A0000D0C0 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 755555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
55555555555555555555555555557

Decimal size = 209
Binary size = 694

Started 01/27/2003 12:00:53 AM
Running time 7s

Candidate certified prime

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

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

5*(10^351-1)/9 + 2*(10^350+1)
== ID:B286A002A18F4 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 755555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555557

Decimal size = 351
Binary size = 1166

Started 01/27/2003 12:45:58 AM
Running time 1mn 51s

Candidate certified prime

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

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

5*(10^423-1)/9 + 2*(10^422+1)
== ID:B286A03D54D16 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 755555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
555555555555555555555555555555555555555555555555555555555555\
557

Decimal size = 423
Binary size = 1405

Started 01/27/2003 05:51:50 PM
Running time 8mn 28s

Candidate certified prime

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

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

5*(10^3813-1)/9 + 2*(10^3812+1)

Primo certificate by courtesy of Ray Chandler (Feb 7, 2013) from factordb.com

http://factordb.com/cert.php?id=1000000000009153836

[PRIMO - Primality Certificate]
Version=4.0.1 - LX64
WebSite=http://www.ellipsa.eu/
Format=3
ID=B36B7021FBBE1
Created=02-04-2013 09:54:00 am
TestCount=503
Status=Candidate certified prime

Put here any comment...

[Running Times]
Initialization=6.55s
1stPhase=27991s
2ndPhase=7273s
Total=35271s

[Candidate]
File=/home/ray/Documents/primo/fdb_knrr/pdp-3813-75w7/primo_1000000000009153836.in

5*(10^3983-1)/9 + 2*(10^3982+1)

Primo certificate by courtesy of Ray Chandler (Feb 7, 2013) from factordb.com

http://factordb.com/cert.php?id=1000000000009154006

[PRIMO - Primality Certificate]
Version=4.0.1 - LX64
WebSite=http://www.ellipsa.eu/
Format=3
Created=02-05-2013 07:49:26 am
TestCount=498
Status=Candidate certified prime

Put here any comment...

[Running Times]
Initialization=7.53s
1stPhase=35558s
2ndPhase=10317s
Total=45883s

[Candidate]
File=/home/ray/Documents/primo/fdb_knrr/pdp-3983-75w7/primo_1000000000009154006.in

5*(10^20925-1)/9 + 2*(10^20924+1)
3-PRP!
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].

5*(10^23787-1)/9 + 2*(10^23786+1)
3-PRP!
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].

5*(10^38853-1)/9 + 2*(10^38852+1)
3-PRP!
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].

5*(10^56043-1)/9 + 2*(10^56042+1)
Ray Chandler / srsieve, PFGW / September 29, 2010.

PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing (68*10^56042+13)/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)
(68*10^56042+13)/9 is Fermat and Lucas PRP! (959.0270s+0.0030s)

5*(10^68505-1)/9 + 2*(10^68504+1)
Ray Chandler / srsieve, PFGW / October 30, 2010.

PFGW Version 3.4.2.64BIT.20101019.Win_Dev [GWNUM 26.4]
Primality testing (68*10^68504+13)/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)
(68*10^68504+13)/9 is Fermat and Lucas PRP! (1547.4805s+0.0144s)

5*(10^74435-1)/9 + 2*(10^74434+1)
Ray Chandler / srsieve, PFGW / November 17, 2010.

PFGW Version 3.4.2.64BIT.20101019.Win_Dev [GWNUM 26.4]
Primality testing (68*10^74434+13)/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 0.01% and helper 0.00% (0.04% proof)
(68*10^74434+13)/9 is Fermat and Lucas PRP! (1692.7921s+0.0019s)

5*(10^205511-1)/9 + 2*(10^205510+1)
By Serge Batalov dd. January 13, 2023.

PRP Source : https://stdkmd.net/nrr/7/75557.htm#prime