def random_prime(bits):
min = 6074001000 << (bits-33)
max = (1<<bits) - 1
while True:
p = randint(min, max)
if(is_prime(p)):
return p
def smaller_closest_prime(x):
if x < 3:
return -100 # no smaller prime
i = 1
while not mr.is_prime(x - i):
i += 1
return (x - i)
def test_first_primes(self):
primes = [2]
for q in xrange(3, 10000, 2):
s = int(ceil(sqrt(q)))
prime = True
for p in primes:
if p > s:
break
if q % p == 0:
prime = False
break
if prime:
primes.append(q)
for p in primes:
self.assertTrue(miller_rabin.is_prime(p))
def generate_test_sequence(
upper_bound): # the test sequence is 2p where p are prime numbers
test_sequence = [
] # the corresponding bit sequence (generated with skip) appeared to be random
num = 1
index = 0
while index < upper_bound:
print('-Generating test sequence:{}%'.format(
round(index * 100 / upper_bound)),
end='\r')
num += 1
if mr.is_prime(num):
test_sequence.append(num * 2)
index += 1
print()
print('test sequence generated')
print()
return test_sequence
# Projecteuler problem 058
# Answer: 26241
from miller_rabin import is_prime
# Ulam spiral
n = 1
diag_total = 1
diag_primes = 0
for i in range(2, 100000, 2):
for j in range(0, 4):
n += i
diag_total += 1
if is_prime(n):
diag_primes += 1
# print (i+1), diag_total, diag_primes, float(diag_primes)/diag_total, n
if diag_primes*10 < diag_total:
print "ans:", i+1
break
from miller_rabin import is_prime
for i in range(3, 1000):
if is_prime(i):
print "%d \n" % i
#i = 2 ** 2048
#while True:
# if is_prime(i):
# print "found prime ! %d " % i
# break
# else:
# i = i - 1
# print "%d \n" % i
import miller_rabin as pt
import math
n = 600851475143
f = n
# find largest odd factor
while f % 2 == 0:
f /= 2
# divide out smallest odd prime factor until f is 1
p = 3
while not f == 1:
while (not pt.is_prime(p) or f % p != 0):
p += 2
while f % p == 0:
f /= p
print(p)
def test_big_composite_integer(self):
self.assertFalse(is_prime(exp_sqr(12456, 10)))
def test_composite_integer(self):
self.assertFalse(is_prime(91))
def test_even_integer(self):
self.assertFalse(is_prime(8))
def test_small_integer(self):
self.assertTrue(is_prime(5))
def test_one(self):
self.assertFalse(is_prime(1))
for i in range(len(primes)):
p = primes[i]
count = 0
while n % p == 0:
n /= p
count += 1
res.append(count)
return res
n = 20
# find all primes <= n
primes = [2]
for p in range(3, n + 1, 2):
if pt.is_prime(p):
primes.append(p)
# initialize the multiplicities
multiplicities = [0 for p in primes]
# find multiplicities of all the primes
for i in range(1, n + 1):
mults = get_multiplicities(primes, i)
for j in range(len(mults)):
if mults[j] > multiplicities[j]:
multiplicities[j] = mults[j]
print(primes)
print(multiplicities)
def larger_closest_prime(x):
i = 1
while not mr.is_prime(x + i):
i += 1
return (x + i)
def test_known_composites(self):
for n in [4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 100]:
self.assertFalse(miller_rabin.is_prime(n))
def test_known_primes(self):
for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 82104551, 452784427,
46897875786625702576864112692857487051,
16924980224899166400812497777709246533,
2345025074052479518600795136681355950888074907685014583790880397468973914695237139661677440025217429981429253627078303444430132992263268824958968314521]:
self.assertTrue(miller_rabin.is_prime(p))
