Question

The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form $2^{6972593}-1$; it contains exactly $2,098,960$ digits. Subsequently other Mersenne primes, of the form $2^p-1$, have been found which contain more digits.

However, in 2004 there was found a massive non-Mersenne prime which contains $2,357,207$ digits: $28433\times2^{7830457}+1$.

Find the last ten digits of this prime number.

Commentary

The gmpy library makes this problem trivial. Using gmpy, this code takes about half a second to run. Without gmpy, well, let’s just say it takes considerably more than a minute to run.

If you’re dealing with large numbers in Python, I highly recommend gmpy.

Python

#!/usr/bin/env python
from gmpy2 import mpz
print(str(mpz(28433*2**7830457+1))[-10:])

$ time python3 non-mersenne.py
real   0m0.364s
user   0m0.363s
sys    0m0.000s