Quote:
Originally Posted by WhoCares
n= some 1523 digits number. I want to check 10^n+7 is prime or not. I have used BigInteger class of c#, and I found that one factor of n is 11, that remains a 1522 digits number. However it seems it will be very long like a lifetime with a standard isPrime() function. Is there any way to do that quickly? (I am open to rent a super computer or something like that)

If you want to determine whether n/11 is prime or composite (n the exponent), ispseudoprime() is much faster than isprime(), although it can only prove compositeness. If you want to determine whether 10^n+7 itself is prime, about all I can suggest offhand is to look for possible small prime factors p, checking whether Mod(10,p)^n + 7 == 0.
I'm not sure how factoring the exponent might help here, but I'm also not sure it won't
;)