def generate_safe_prime(bits):
while True:
print 'trying prime'
p_ = millerrabin.generateLargePrime(bits-1)
if type(p_) is str:
print 'failed to find prime, trying again'
continue
p = 2*p_ + 1
if millerrabin.is_probable_prime(p):
return p
else:
'not a safe prime, trying again'
def generate_safe_prime(bits):
while True:
print 'trying prime'
p_ = millerrabin.generateLargePrime(bits - 1)
if type(p_) is str:
print 'failed to find prime, trying again'
continue
p = 2 * p_ + 1
if millerrabin.is_probable_prime(p):
return p
else:
'not a safe prime, trying again'
def totient(n):
"""
>>> totient(20)
8
>>> totient(97)
96
>>> totient(56)
24
"""
if is_probable_prime(n):
return n - 1
f = factors(n)
# use (p - 1) / p instead of 1 - 1./p to avoid floating point error
return n * reduce(mul, ((p - 1) for p in f)) / reduce(mul, f)
def totient(n):
"""
>>> totient(20)
8
>>> totient(97)
96
>>> totient(56)
24
"""
if is_probable_prime(n):
return n - 1
f = factors(n)
# use (p - 1) / p instead of 1 - 1./p to avoid floating point error
return n * reduce(mul, ( (p-1) for p in f )) / reduce(mul, f)
def factors(number):
"""
>>> factors(3)
[3]
>>> factors(4)
[2]
>>> factors(6)
[2, 3]
>>> factors(12)
[2, 3]
"""
if is_probable_prime(number):
return [number]
for p in generator():
if number % p == 0:
while number % p == 0:
number = number / p
if number == 1:
return [p]
else:
return [p] + factors(number)
def factors(number):
"""
>>> factors(3)
[3]
>>> factors(4)
[2]
>>> factors(6)
[2, 3]
>>> factors(12)
[2, 3]
"""
if is_probable_prime(number):
return [number]
for p in generator():
if number % p == 0:
while number % p == 0:
number = number / p
if number == 1:
return [p]
else:
return [p] + factors(number)
from millerrabin import is_probable_prime # .8s instead of 130s using is_prime
n = 1 # circle counter
total = 1 # 1 at the center belongs to all diagonal
prime = 0
while True:
for i in (0, 2, 4, 6):
# testing diagonal values for primality
if is_probable_prime((2 * n + 1)**2 - i * n):
prime += 1
total += 1
# testing ratio
if prime * 100 / total < 10:
# the side lenght is ...
print 2 * n + 1
break
# next circle
n += 1
from millerrabin import is_probable_prime # .8s instead of 130s using is_prime
n = 1 # circle counter
total = 1 # 1 at the center belongs to all diagonal
prime = 0
while True:
for i in (0, 2, 4, 6):
# testing diagonal values for primality
if is_probable_prime( (2 * n + 1) ** 2 - i * n ):
prime += 1
total += 1
# testing ratio
if prime * 100 / total < 10:
# the side lenght is ...
print 2 * n + 1
break
# next circle
n += 1
def valid(a, b):
s1 = str(a)+str(b)
s2 = str(b)+str(a)
if is_probable_prime(int(s1)) and is_probable_prime(int(s2)):
return True
return False
