Using Pari/gp (< 1s)
gp > isprime(4*(10^5-1)/9+5*10^4+5*10^2+5)
%1 = 1
Using Pari/gp (< 1s)
gp > isprime(4*(10^11-1)/9+5*10^10+5*10^5+5)
%1 = 1
Using Pari/gp (< 1s)
gp > isprime(4*(10^17-1)/9+5*10^16+5*10^8+5)
%1 = 1
Using Pari/gp (< 1s)
gp > isprime(4*(10^43-1)/9+5*10^42+5*10^21+5)
%1 = 1
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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