def test_pollard_p1_2(self):
p = list(primes(10))
prime_factors = random.choices(p, k=5)
num = product(prime_factors)
found_factors = factor(num, 'pollard-p1')
self.assertEqual(num, product(found_factors))
self.assertCountEqual(found_factors, prime_factors)
def test_pollard_rho_1(self):
# Taken from Wikipedia
num = 8051
f = factor(num, 'pollard-rho')
self.assertCountEqual(f, [97, 83])
prime_factors = [13, 19, 37]
num = product(prime_factors)
found_factors = factor(num, 'pollard-rho')
self.assertEqual(num, product(found_factors))
self.assertCountEqual(found_factors, [13, 19, 37])
def test_fermat_factor_2(self):
prime_factors = [13, 19, 37]
num = product(prime_factors)
found_factors = factor(num, 'fermat')
self.assertEqual(num, product(found_factors))
self.assertCountEqual(found_factors, [13, 19, 37])
# A random composite number picked from nowhere.
num = 124987921
found_factors = factor(num, 'fermat')
self.assertEqual(num, product(found_factors))
self.assertCountEqual(found_factors, [690541, 181])
def test_gnu_factor(self):
# test the toolchain, not the algorithm...
# A random composite number picked from nowhere.
num = 124987921
found_factors = factor(num, 'gnu-factor')
self.assertEqual(num, product(found_factors))
self.assertCountEqual(found_factors, [690541, 181])
def jacobi(a, n):
"""
The Jacobi Symbol of `a` mod `n`
Implemented by factoring `a` and multiplying powers of each factor's Legendre symbol to get
the Jacobi Symbol of `a`.
Example:
>>> jacobi(4567, 12345)
-1
>>> jacobi(107, 137)
1
"""
factors = Counter(factor(n, 'pollard-p1'))
return product(legendre(a, f)**b for f, b in factors.items())
def test_trial_division_factor(self):
prime_factors = [13, 13, 19, 37, 113]
num = product(prime_factors)
found_factors = factor(num, 'trial-division')
self.assertCountEqual(prime_factors, found_factors)
def main():
"""Test whether a product of the first n primes, plus 1 is prime. Very few are..."""
for i in range(1, 101):
p = product(primes(i)) + 1
print(i, is_prime(p))