def f(a, b, p):
if b == 1 or p == 2: return a % p
x = f(a, b-1, phi(p))
return pow_mod(a, x, p)
#https://github.com/skydark/project-euler/blob/master/129.py
from time import time; t=time()
from mathplus import pow_mod, factorization, phi
M = 1000000
S = M//2*2 + 1
T = 1001000
def report(p):
print(p)#, time()-t)
import sys
sys.exit()
for p in range(S, T, 2):
if p % 5 == 0: continue
phip = phi(p)
m = p
if p % 3 == 0:
phip *= 9
m *= 9
if phip <= M: continue
factors = factorization(phip)
while phip > M:
for f, c in factors:
phif = phip//f
if pow_mod(10, phif, m) == 1:
phip = phif
if c > 1:
factors = [(k, v) if k != f else (k, v-1)
for k, v in factors]
else:
def f(a, b, p):
if b == 1 or p == 2: return a % p
x = f(a, b - 1, phi(p))
return pow_mod(a, x, p)