How much time (in hours) will it take to check if the number with 20 binary digits is the prime number?
Primality testing is very fast with the Miller–Rabin algorithm [1]. You can use the deterministic variant with witnesses 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37 to test any 64 bit number in $O(\log^3 n)$ time. This should take less than one second with any reasonable implementation.

[1] https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test