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


4*(1011-1)/9 + 5*1010 + 5*105 + 5
Using Pari/gp (< 1s)
     gp > isprime(4*(10^11-1)/9+5*10^10+5*10^5+5)
     %1 = 1


4*(1017-1)/9 + 5*1016 + 5*108 + 5
Using Pari/gp (< 1s)
     gp > isprime(4*(10^17-1)/9+5*10^16+5*10^8+5)
     %1 = 1


4*(1043-1)/9 + 5*1042 + 5*1021 + 5
Using Pari/gp (< 1s)
     gp > isprime(4*(10^43-1)/9+5*10^42+5*10^21+5)
     %1 = 1


4*(101021-1)/9 + 5*101020 + 5*10510 + 5
Using Pari/gp (time = 1min, 47,610 ms)
     gp > default(parisizemax,"1G")
     gp > isprime(4*(10^1021-1)/9+5*10^1020+5*10^510+5)
     %1 = 1









 

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