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
def testIntegralPower(self): self.assertEquals(0, number.integralPower(1)) self.assertEquals(0, number.integralPower(2)) self.assertEquals(0, number.integralPower(3)) self.assertEquals(1, number.integralPower(4)) self.assertEquals(0, number.integralPower(24), "5^2 - 1") self.assertEquals(1, number.integralPower(25), "5^2") self.assertEquals(0, number.integralPower(26), "5^2 + 1") self.assertEquals(0, number.integralPower(31), "2^5 - 1") self.assertEquals(1, number.integralPower(32), "2^5") self.assertEquals(0, number.integralPower(33), "2^5 + 1") self.assertEquals(0, number.integralPower(16806), "7^5 - 1") self.assertEquals(1, number.integralPower(16807), "7^5") self.assertEquals(0, number.integralPower(16808), "7^5 + 1")
