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")