def primes(n):
# 1
if number.integralPower(n):
return 0
# 2
r = 2
# 3
while r < n:
# 4
if number.gcd(n, r) != 1:
return 0
# 5
if r in number.SMALL_PRIMES:
# 6
factors = number.factor(r - 1)
if len(factors) == 0:
q = 0 # hack
else:
q = factors[-1]
# 7
if (q >= 4 * math.sqrt(r) * number.lg(n)) and (number.modPow(n, (r - 1) / q, r) != 1):
# 8
break
# 9
r = r + 1
# 10
print "r for ", n, ":", r
return r
# 11
#for a in range(1, int(2 * math.sqrt(r) * number.lg(n)) + 2)):
# 12
#poly = [-1] + [0] * (r - 1) + [1]
#lhs = polynomial.modPow([-a, 1], n, poly)
#rhs = polynomial.mod([-a] + [0] * (n - 1) + [1], poly)
#if lhs != rhs:
# return 0
# 13
return 1
# 10
print "r for ", n, ":", r
return r
# 11
#for a in range(1, int(2 * math.sqrt(r) * number.lg(n)) + 2)):
# 12
#poly = [-1] + [0] * (r - 1) + [1]
#lhs = polynomial.modPow([-a, 1], n, poly)
#rhs = polynomial.mod([-a] + [0] * (n - 1) + [1], poly)
#if lhs != rhs:
# return 0
# 13
return 1
if __name__ == '__main__':
#print primes(9901)
print 2 * math.sqrt(10000) * number.lg(10000)
print number.factor(17902)
print 2 * math.sqrt(17903) * number.lg(99991)
#print primes(99991)
#for n in number.SMALL_PRIMES:
# if n != primes(n):
# break
