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

Using Pari/gp (< 1s)
     gp > isprime((10^17-1)/9+8*10^16+8*10^8+8)
     %1 = 1

Using Pari/gp (< 1s)
     gp > isprime((10^61-1)/9+8*10^60+8*10^30+8)
     %1 = 1

Using Pari/gp (< 1s)
     gp > isprime((10^95-1)/9+8*10^94+8*10^47+8)
     %1 = 1

Using Pari/gp (< 1s)
     gp > isprime((10^119-1)/9+8*10^118+8*10^59+8)
     %1 = 1

Using Pari/gp (< 1s)
     gp > isprime((10^139-1)/9+8*10^138+8*10^69+8)
     %1 = 1

Using Pari/gp (< 1s)
     gp > isprime((10^169-1)/9+8*10^168+8*10^84+8)
     %1 = 1

Using Pari/gp (time = 24min, 42,594 ms)
     gp > default(parisizemax,"1G")
     gp > isprime((10^1913-1)/9+10^1912*8+10^956*8+8)
     %1 = 1

Proven by certificate by Masaki UKAI (August 22, 2022)
http://factordb.com/index.php?id=1100000002736129756

C:\pfgw>pfgw64 -q"(10^11011-1)/9+8*10^11010+8*10^5505+8"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

(10^11011-1)/9+8*10^11010+8*10^5505+8 is 3-PRP! (0.7360s+0.0004s)

Note that its length, i.e. 11011, is palindromic as well!

C:\pfgw>pfgw64 -q"(10^12539-1)/9+8*10^12538+8*10^6269+8"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

(10^12539-1)/9+8*10^12538+8*10^6269+8 is 3-PRP! (0.8442s+0.0009s)

C:\pfgw>pfgw64 -q"(10^18583-1)/9+8*10^18582+8*10^9291+8"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

(10^18583-1)/9+8*10^18582+8*10^9291+8 is 3-PRP! (1.6775s+0.0007s)

C:\pfgw>pfgw64 -q"(10^43535-1)/9+8*10^43534+8*10^21767+8"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

(10^43535-1)/9+8*10^43534+8*10^21767+8 is 3-PRP! (11.3079s+0.0005s)