"""Verifier: any nontrivial factor of the Mersenne number M1277 = 2**1277 - 1.

No factor of M1277 is publicly known; it is the smallest Mersenne number with prime
exponent whose factorization status is entirely open.

Solution format: one positive integer d.
Accepted iff 1 < d < N and d divides N. Primality of d is not required.
"""

N = 2**1277 - 1


def verify(solution: str, rng) -> bool:
    s = solution.strip()
    if not s.isdigit():
        return False
    d = int(s)
    return 1 < d < N and N % d == 0