2*(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=(72*10^3-27)/99
N=727
*** N is prime!
Time: 0 sec

2*(10^5-1)/9 + 5*(10^4+1)
run"aprt-cle
Test number  N=? 72227

Preparatory test
Pass !

72227 is prime.
0:00:00
OK

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

2*(10^9-1)/9 + 5*(10^8+1)
run"aprt-cle
Test number  N=? 722222227

Preparatory test
Pass !

722222227 is prime.
0:00:00
OK

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

2*(10^29-1)/9 + 5*(10^28+1)

== ID:B286500F8D284 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 72222222222222222222222222227

Decimal size = 29
Binary size = 96

-----------------------------------------------------------------
1) N-1 Test
-----------------------------------------------------------------
N = Candidate
S = 24178
R = 2987104897932923410630417
B = 2

-----------------------------------------------------------------
2) N+1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 2
R = 1493552448966461705315209
Q = 14

-----------------------------------------------------------------
3) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 7101297
R = 210321079229440261
A = 0
B = 16
T = 2

-----------------------------------------------------------------
4) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 73980
R = 2842945109887
B = 2

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

Started 01/22/2003 04:31:46 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.

2*(10^65-1)/9 + 5*(10^64+1)
== ID:B2869006422BA =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 722222222222222222222222222222222222222222222222222222222222\
22227

Decimal size = 65
Binary size = 216

Started 01/26/2003 01:49:22 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.

2*(10^725-1)/9 + 5*(10^724+1)
[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286D03FF84FA
Created=01/30/2003 06:37:57 PM
TestCount=119
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\pdp727_725.in
Expression=2*(10^725-1)/9 + 5*(10^(723+1)+1)
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
HexadecimalSize=602 DecimalSize=725 BinarySize=2408 [Running Times] Initialization=1.44s 1stPhase=1h 35mn 36s 2ndPhase=17mn 20s Total=1h 52mn 58s Proved prime with 'Primo 2.0.0 - beta 3' by Patrick De Geest using a Pentium III 650 MHz chip.

2*(10^1787-1)/9 + 5*(10^1786+1)
[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B290C02E07C87
Created=07/08/2003 01:24:31 PM
TestCount=253
Status=Candidate certified prime

[Running Times]
Initialization=5.11s
1stPhase=12h 13mn 36s
2ndPhase=50mn 19s
Total=13h 4mn 1s

[Candidate]
File=C:\Primo IN & OUT files\PDP1787.in
Expression=2*(10^1787-1)/9+5*(10^1786+1)
HexadecimalSize=1484 DecimalSize=1787 BinarySize=5936 Proved prime with 'Primo 2.1.1' by Patrick De Geest using a 3000 MHz Pentium 4 cpu. Certificate Primo-B290C02E07C87-01.out available by simple email request (337 KB).

2*(10^7277-1)/9 + 5*(10^7276+1)
Xinyao Chen informs me (May 19,2022) that this number is
now a proven palindromic plateau & depression prime.
Proof was done by Maksym Voznyy on November 30, 2020.

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

2*(10^19463-1)/9 + 5*(10^19462+1)
3-PRP!

2*(10^24215-1)/9 + 5*(10^24214+1)
3-PRP!
PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8].

2*(10^51779-1)/9 + 5*(10^51778+1)
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing (65*10^51778+43)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 1+sqrt(5)
(65*10^51778+43)/9 is Fermat and Lucas PRP! (1532.2989s+0.0028s)

2*(10^131393-1)/9 + 5*(10^131392+1)
By Tyler Busby dd. January 11, 2023.

Source : https://stdkmd.net/nrr/7/72227.htm#prime