8*(105-1)/9 - 7*104 - 7*102 - 7
Using Pari/gp (< 1s)
     gp > isprime(8*(10^5-1)/9-7*10^4-7*10^2-7)
     %1 = 1


8*(107-1)/9 - 7*106 - 7*103 - 7
Using Pari/gp (< 1s)
     gp > isprime(8*(10^7-1)/9-7*10^6-7*10^3-7)
     %1 = 1


8*(10293-1)/9 - 7*10292 - 7*10146 - 7
Using Pari/gp (1,376 ms)
     gp > isprime(8*(10^293-1)/9-7*10^292-7*10^146-7)
     %1 = 1


8*(10511-1)/9 - 7*10510 - 7*10255 - 7
Using Pari/gp (6,641 ms)
     gp > default(parisizemax,"1G")
     gp > isprime(8*(10^511-1)/9-7*10^510-7*10^255-7)
     %1 = 1


8*(103257-1)/9 - 7*103256 - 7*101628 - 7
Proven by certificate by Robert Gelhar (June 6, 2020)
http://factordb.com/index.php?id=1100000001521765026


8*(103629-1)/9 - 7*103628 - 7*101814 - 7
C:\pfgw>pfgw64 -q"8*(10^3629-1)/9-7*10^3628-7*10^1814-7"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

8*(10^3629-1)/9-7*10^3628-7*10^1814-7 is 3-PRP! (0.0733s+0.0003s)
 

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