4*(105-1)/9 + 3*104 + 3*102 + 3
Using Pari/gp (< 1s)
     gp > isprime(4*(10^5-1)/9+3*10^4+3*10^2+3)
     %1 = 1


4*(10245-1)/9 + 3*10244 + 3*10122 + 3
Using Pari/gp (time = 1,063 ms)
     gp > default(parisizemax,"1G")
     gp > isprime(4*(10^245-1)/9+3*10^244+3*10^122+3)
     %1 = 1


4*(101043-1)/9 + 3*101042 + 3*10521 + 3
Using Pari/gp (+/- 1 min 37s)
     gp > default(parisizemax,"1G")
     gp > isprime(4*(10^1043-1)/9+3*10^1042+3*10^521+3)
     %1 = 1


4*(102531-1)/9 + 3*102530 + 3*101265 + 3
Proven by certificate by Masaki UKAI (October 21, 2022)
http://factordb.com/index.php?id=1100000002736129758


4*(103563-1)/9 + 3*103562 + 3*101781 + 3
C:\pfgw>pfgw64 -q"4*(10^3563-1)/9+3*10^3562+3*10^1781+3"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

4*(10^3563-1)/9+3*10^3562+3*10^1781+3 is 3-PRP! (0.0719s+0.0003s)
 

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