2*(107-1)/9 - 106 - 103 - 1
Using Pari/gp (< 1s)
     gp > isprime(2*(10^7-1)/9-10^6-10^3-1)
     %1 = 1


2*(1011-1)/9 - 1010 - 105 - 1
Using Pari/gp (< 1s)
     gp > isprime(2*(10^11-1)/9-10^10-10^5-1)
     %1 = 1


2*(1025-1)/9 - 1024 - 1012 - 1
Using Pari/gp (< 1s)
     gp > isprime(2*(10^25-1)/9-10^24-10^12-1)
     %1 = 1


2*(104787-1)/9 - 104786 - 102393 - 1
Proven by certificate by Masaki UKAI (February 27, 2020)
http://factordb.com/index.php?id=1100000001357288793


2*(1037631-1)/9 - 1037630 - 1018815 - 1
C:\pfgw>pfgw64 -q"2*(10^37631-1)/9-10^37630-10^18815-1"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

2*(10^37631-1)/9-10^37630-10^18815-1 is 3-PRP! (7.9134s+0.0005s)
 

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