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

Using Pari/gp (< 1s)
     gp > isprime(8*(10^11-1)/9-10^10-10^5-1)
     %1 = 1

Using Pari/gp (< 1s)
     gp > default(parisizemax,"1G")
     gp > isprime(8*(10^257-1)/9-10^256-10^128-1)
     %1 = 1

Using Pari/gp (time = 19,892 ms)
     gp > default(parisizemax,"1G")
     gp > isprime(8*(10^661-1)/9-10^660-10^330-1)
     %1 = 1

Using Pari/gp (time = 17min, 27,828 ms)
     gp > default(parisizemax,"1G")
     gp > isprime(8*(10^1609-1)/9-10^1608-10^804-1)
     %1 = 1

C:\pfgw>pfgw64 -q"8*(10^3683-1)/9-10^3682-10^1841-1"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

8*(10^3683-1)/9-10^3682-10^1841-1 is 3-PRP! (0.0750s+0.0003s)