def main():
p = Prime()
p.sieve(100000000)
primes = p.primes()
print("sieve done")
search(p, tuple(), 5, 0)
print(p.counter)
def main():
p = Prime()
p.sieve(100000000)
primes = p.primes()
print("sieve done")
search(p, tuple(), 5, 0)
print(p.counter)
def main():
p = Prime()
n = 1000000
sieve = [False] * n
naive = [False] * n
with Timer('naive'):
for i in range(n):
naive[i] = is_prime(i)
with Timer('sieve'):
p.sieve(n)
for i in range(n):
sieve[i] = p.is_prime(i)
def main():
p = Prime()
n = 1000000
sieve = [False] * n
naive = [False] * n
with Timer('naive'):
for i in range(n):
naive[i] = is_prime(i)
with Timer('sieve'):
p.sieve(n)
for i in range(n):
sieve[i] = p.is_prime(i)
def search(p: Prime, t: tuple, r: int, first: int):
if len(t) < r:
for i, p1 in enumerate(islice(p.primes(), first, 2000)):
t1 = t + (p1, )
if all(concatable_primes(p, t1)):
search(p, t1, r, first=i)
else:
print(t)
def search(p: Prime, t: tuple, r: int, first: int):
if len(t) < r:
for i, p1 in enumerate(islice(p.primes(), first, 2000)):
t1 = t + (p1,)
if all(concatable_primes(p, t1)):
search(p, t1, r, first=i)
else:
print(t)
def test_generate1(self):
"""prime generator 1"""
p = Prime()
self.assertEqual(self.c, list(p[:len(self.c)]))
def test_init4(self):
"""remove multiples of 2-3-5-7"""
p = Prime(4)
self.assertEqual(self.c[:4], list(p.table))
self.assertEqual(self.c[4:30], list(islice(p.sieve, 26)))
self.assertEqual(121, next(p.sieve))
def test_init3(self):
"""remove multiples of 2-3-5"""
p = Prime(3)
self.assertEqual(self.c[:3], list(p.table))
self.assertEqual(self.c[3:15], list(islice(p.sieve, 12)))
self.assertEqual(49, next(p.sieve))
def test_init2(self):
"""remove multiples of 2-3"""
p = Prime(2)
self.assertEqual(self.c[:2], list(p.table))
self.assertEqual(self.c[2:9], list(islice(p.sieve, 7)))
self.assertEqual(25, next(p.sieve))
def test_init1(self):
"""remove multiples of 2"""
p = Prime(1)
self.assertEqual(self.c[:1], list(p.table))
self.assertEqual(self.c[1:4], list(islice(p.sieve, 3)))
self.assertEqual(9, next(p.sieve))
def test_factorize2(self):
"""prime factorization 2"""
p = Prime()
self.assertEqual([99991, 100003], list(p.factorize(9999399973)))
from itertools import count, combinations
from fractions import Fraction, gcd
from tqdm import tqdm
from primes import Prime
prime = Prime()
prime.sieve(1000000)
def factor(n):
idx = 0
primes = prime.primes()
while n > 1:
idx = next(i for i in count(idx) if n % primes[i] == 0)
yield primes[idx]
n //= primes[idx]
def product(iterable):
tmp = 1
for x in iterable:
tmp *= x
return tmp
def facit(d):
return sum(1 for n in range(1, d) if gcd(n, d) == 1)
def R(d):
factors = set(factor(d))
resilient = d
s = -1
def test_generate2(self):
"""prime generator 2"""
p = Prime()
self.assertEqual(131071, p[12250])
def main():
prime = Prime()
#print(prime.is_prime(987654321))
print(max(p for p in iter_pandigitals() if prime.is_prime(p)))
def main():
prime = Prime()
#print(prime.is_prime(987654321))
print(max(p for p in iter_pandigitals() if prime.is_prime(p)))
from fractions import Fraction
from tqdm import tqdm
from primes import Prime
prime = Prime()
prime.sieve(1000000)
def product(v):
r = 1
for e in v:
r *= e
return r
def φ(n):
factors = set(prime.factor(n))
return n * product(f - 1 for f in factors) // product(factors)
def main(i):
def maximizer(x):
return Fraction(x, φ(x))
print(max((n for n in tqdm(range(2, i + 1))), key=maximizer))
main(1000000)
def test_isprime3(self):
"""primality test 3"""
p = Prime()
self.assertTrue(99999989 in p)
self.assertTrue(999999999989 in p)
def test_isprime4(self):
"""primality test 4"""
p = Prime()
self.assertTrue(9999399973 not in p)
def test_factorize1(self):
"""prime factorization 1"""
p = Prime()
self.assertEqual([2, 2, 3, 3, 5, 5], list(p.factorize(900)))
from fractions import Fraction
from itertools import combinations
from tqdm import tqdm
from primes import Prime
prime = Prime()
prime.sieve(10000000 // 2)
#prime.sieve(100000)
def product(v):
r = 1
for e in v:
r *= e
return r
def φ(n):
factors = set(prime.factor(n))
return n * product(f - 1 for f in factors) // product(factors)
def is_permutation(a, b):
return sorted(str(a)) == sorted(str(b))
def quick_totients(rmax):
for r in range(1, rmax):
print(r)
for factors in combinations(prime.primes(), r):