def test1():
per = 10**5
core = compute_period_product(per)
print 'aa', core
print 'ref', (factorial(per)/10**prime_factor_expo_of_factorial(per, 5))%per
print 'result', modexp(core, 10**7, per)
def compute_period_product(period):
prod = 1
niu = prime_factor_expo_of_factorial(period, 5)
for x in xrange(1, period + 1):
_, five_rst = partial_factor(x, 5)
x = five_rst
if niu > 0:
two_e, two_rst = partial_factor(x, 2)
if two_e > 0:
if niu >= two_e:
niu -= two_e
x = two_rst
else:
two_e = two_e - niu
niu = 0
x = two_rst * modexp(2, two_e, period)
prod = (prod * x) % period
# print x, prod
return prod
# -*- coding: utf8 -*- """ The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 26972593−1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2p−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: 28433×2**7830457+1. Find the last ten digits of this prime number. """ from sieve import modexp print (28433 * modexp(2, 7830457, 10**10) + 1)%10**10