def testFactorizeLargePrimes(self): random_obj = intalg.MiniIntRandom(42) for ps in ([1073741827, 1152921504606847009], [34359738421, 1180591620717411303449], [7, 1763668414462081], [100003], [10000000019], [1000000000039], # Slow but tolerable. [10000000019] * 9, [1000000007] * 10, [1000000007] + [1000000009] * 2 + [1000000021] * 3): n = 1 for p in ps: n *= p divisors = set() # All divisors based on ps, except for 1. for i in xrange(1, 1 << len(ps)): r = 1 for j in xrange(0, len(ps)): if i & (1 << j): r *= ps[j] divisors.add(r) r = intalg.brent(n, random_obj) assert r in divisors r = intalg.pollard(n, random_obj) assert r in divisors sps = intalg.finder_slow_factorize(n) assert sps == ps, (n, sps, ps) sps = intalg.factorize(n) assert sps == ps, (n, sps, ps)
def testFactorizeLargePrimes(self): random_obj = intalg.MiniIntRandom(42) for ps in ( [1073741827, 1152921504606847009], [34359738421, 1180591620717411303449], [7, 1763668414462081], [100003], [10000000019], [1000000000039], # Slow but tolerable. [10000000019] * 9, [1000000007] * 10, [1000000007] + [1000000009] * 2 + [1000000021] * 3): n = 1 for p in ps: n *= p divisors = set() # All divisors based on ps, except for 1. for i in xrange(1, 1 << len(ps)): r = 1 for j in xrange(0, len(ps)): if i & (1 << j): r *= ps[j] divisors.add(r) r = intalg.brent(n, random_obj) assert r in divisors r = intalg.pollard(n, random_obj) assert r in divisors sps = intalg.finder_slow_factorize(n) assert sps == ps, (n, sps, ps) sps = intalg.factorize(n) assert sps == ps, (n, sps, ps)
def testBrentComposite(self): random_obj = intalg.MiniIntRandom(42) for n in intalg.yield_composites(): if n > 100000: break b = intalg.brent(n, random_obj) assert b > 1 assert b <= n self.assertEquals(0, n % b, (b, n))
def testBrentPrime(self): random_obj = intalg.MiniIntRandom(42) for n in intalg.primes_upto(100000): b = intalg.brent(n, random_obj) self.assertEquals(b, n)