How much time (in hours) will it take to check if the number with 20 binary digits is the prime number? How much time (in hours) will it take to check if the number with 20 binary digits is the prime number, in problem it's mentioned that for number with 10 digits it took 1 hour it's also said that the number has been checked using AKS pirmality test and it's also given that log(n) is the lenght of the number to be verified.
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