UVA 583 分解质因数

Webster defines prime as:
prime (prim) n. [ME, fr. MF, fem. of prin first, L primus; akin to L prior] 1: first in
time: original 2 a: having no factor except itself and one ⟨3 is a number⟩ b : having
no common factor except one ⟨12 and 25 are relatively ⟩ 3 a: first in rank, authority or
significance: principal b: having the highest quality or value ⟨ television time ⟩ [from
Webster’s New Collegiate Dictionary]
The most relevant definition for this problem is 2a: An integer g > 1 is said to be prime if and only
if its only positive divisors are itself and one (otherwise it is said to be composite). For example, the
number 21 is composite; the number 23 is prime. Note that the decompositon of a positive number g
into its prime factors, i.e.,
g = f1 f2 fn
is unique if we assert that fi > 1 for all i and fi fj for i < j.
One interesting class of prime numbers are the so-called Mersenne primes which are of the form
2p