def find1(N, A=None):
if A == None:
A = gmpy.mpz(gmpy.sqrt(N) + 1)
k = A * A - N
assert gmpy.is_power(k)
x = gmpy.sqrt(A * A - N)
p, q = A - x, A + x
#print p
#print q
assert gmpy.is_prime(p)
assert gmpy.is_prime(q)
assert p * q == N
return p, q
def find1(N, A = None):
if A == None:
A = gmpy.mpz(gmpy.sqrt(N)+1)
k = A*A - N
assert gmpy.is_power(k)
x = gmpy.sqrt(A*A - N)
p, q = A - x, A + x
#print p
#print q
assert gmpy.is_prime(p)
assert gmpy.is_prime(q)
assert p*q==N
return p, q
def find3(N, A=None):
if A == None:
A = gmpy.mpz(gmpy.sqrt(24 * N) + 1)
k = A * A - 24 * N
assert gmpy.is_power(k)
x = gmpy.sqrt(k)
print x
q1 = (A - x) / 4
p1 = (A + x) / 6
q2 = (A + x) / 4
p2 = (A - x) / 6
if gmpy.is_prime(p1) and gmpy.is_prime(q1) and p1 * q1 == N:
return p1, q1
elif gmpy.is_prime(p2) and gmpy.is_prime(q2) and p2 * q2 == N:
return p2, q2
else:
assert False
def find3(N, A = None):
if A == None:
A = gmpy.mpz(gmpy.sqrt(24*N)+1)
k = A*A - 24*N
assert gmpy.is_power(k)
x = gmpy.sqrt(k)
print x
q1 = (A - x)/4
p1 = (A + x)/6
q2 = (A + x)/4
p2 = (A - x)/6
if gmpy.is_prime(p1) and gmpy.is_prime(q1) and p1*q1==N:
return p1, q1
elif gmpy.is_prime(p2) and gmpy.is_prime(q2) and p2*q2==N:
return p2, q2
else:
assert False