def is_factor_R_10_n(p):
"""测试p是否是R(10**n) {n 为自然数}的因子
>>> is_factor_R_10_n(3)
False
>>> is_factor_R_10_n(11)
True
>>> is_factor_R_10_n(17)
True
>>> is_factor_R_10_n(41)
True
>>> is_factor_R_10_n(73)
True
"""
print p
# g(k) = sum(a[k] ** i for i in range(10)) % p
# a[0] = 10
# a[n] = 10 ** (10 ** n)
# a[n + 1] = 10 ** (10 ** (n + 1)) = 10 ** ((10 ** n) * 10) = a[n] ** 10
a = 10
is_cycle = set()
while True:
if sum(exp_mod(a, i, p) for i in range(10)) % p== 0:
return True
if a % p in is_cycle:
return False
is_cycle.add(a % p)
a = exp_mod(a, 10, p)
def fg(begin, end, step = 1):
assert end > begin
assert step in (1, 2)
if begin > 100000:
a = begin / 100000
begin = begin - a * 100000
end = end - a * 100000
result = 1
if end - begin > 100000:
result *= exp_mod(h(_f(range(begin, begin + 100000, step))), (end - begin) / 100000, 100000)
return result * h(_f(range(begin, end - (((end - begin) / 100000) * 100000), step)))
def _primality_test(n):
x = randint(2, n - 1)
k = 0
q = n - 1
while q % 2 == 0:
k += 1
q /= 2
j = 0
y = exp_mod(x, q, n)
while j < k:
if y == n - 1 or (y == 1 and j == 0):
return True
if y == 1 and j > 0:
return False
j += 1
y = (y * y) % n
return y == 1
def f(n):
"""
>>> f(9)
36288
>>> f(10)
36288
>>> f(20)
17664
>>> f(25)
85984
>>> f(50)
60512
"""
if n <= 10 ** 5:
return h(range(1, n + 1))
elif n % 10 == 0:
x,y = exp_mod(V, (n / (5 ** 5)), 100000) , f(n / 5)
print x,y
return g(x * y)
