def main():
''' Driver function '''
for n in count(1, 1):
p = primes_nth(n)
p_sqr = p**2
rem = (pow(p - 1, n, p_sqr) + pow(p + 1, n, p_sqr)) % p_sqr
if rem > 10**10:
print(n)
break
def get_mapped_prime(self, token: str):
prime = self.opcode_to_prime.get(token)
if prime:
pass
else:
helper_hash = hashlib.blake2b(digest_size=3)
helper_hash.update(token)
prime = pyprimesieve.primes_nth(int(helper_hash.hexdigest(), 16))
self.opcode_to_prime[token] = prime
return prime
def sum_S_to(n):
''' Returns the sum of values of S (as described in the problem) for all
consecutive primes p1 and p2, p2 > p1 and 5 <= p1 <= n '''
total = 0
primes = primes_to(n)
# Get p2 for last p1
primes += [primes_nth(len(primes) + 1)]
# The lowest positive value of n that satisfies both n = 0 (mod p2) and
# n = p1 (mod 10**k) (k being the number of digits in p1) is S for that
# pair of primes. The function (easily derived from modular relations)
# n(x) = pow_10*(x*p2 - p1*pow_10_mult_inv) + p1
# (pow_10 is 10**k and pow_10_mult_inv is the multiplicative inverse of
# 10**k mod p2) produces all valid values of n for a given p1,p2 pair
for p1, p2 in zip(primes[2:-1], primes[3:]):
p1_digits = int(log(p1, 10)) + 1
pow_10 = 10**p1_digits
pow_10_mult_inv = pow(pow_10, -1, p2)
# Find the lowest value of x for which n(x) is positive
x = int((-p1 / pow_10 + p1 * pow_10_mult_inv) / p2) + 1
total += pow_10 * (x * p2 - p1 * pow_10_mult_inv) + p1
return total
def test_smallnums_1(self):
self.assertEqual(pyprimesieve.primes_nth(1), 2)
def test_bignums_3(self):
self.assertEqual(pyprimesieve.primes_nth(81749371), 1648727417)
def test_bignums_2(self):
self.assertEqual(pyprimesieve.primes_nth(94949), 1228567)
def test_bignums_1(self):
self.assertEqual(pyprimesieve.primes_nth(10001), 104743)
def test_smallnums_2(self):
self.assertEqual(pyprimesieve.primes_nth(4), 7)
def ps_nth_super(nth):
return primes_nth(nth)
def _hash_char(val: str) -> int:
if len(val) > 1:
raise ValueError("char length must be 1")
idx = ord(val)
return primes_nth(idx)
def _get_hash(val) -> int:
if isinstance(val, int):
return primes_nth(val)
elif isinstance(val, str):
return reduce(lambda x, y: x * _hash_char(y), val, 1)
import string
import math
from random import randrange
import pyprimesieve as pp
# Possible digits from the lowest to the highest
DIGITS = '%s%s' % (string.digits, string.ascii_lowercase)
PRIMES = [pp.primes_nth(idx) for idx in range(1, 501)]
small_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] # etc.
def probably_prime(n, k):
"""Return True if n passes k rounds of the Miller-Rabin primality
test (and is probably prime). Return False if n is proved to be
composite.
"""
if n < 2:
return False
for p in small_primes:
if n < p * p:
return True
if n % p == 0:
return False
r, s = 0, n - 1
while s % 2 == 0:
r += 1
s //= 2
for _ in range(k):
a = randrange(2, n - 1)
x = pow(a, s, n)
def test_exception_2(self):
with self.assertRaises(ValueError):
pyprimesieve.primes_nth(-1111)
from pyprimesieve import primes_nth print primes_nth(10001)
def getSolution(limit):
return pyprimesieve.primes_nth(limit)
def test_exception_2(self):
with self.assertRaises(ValueError):
pyprimesieve.primes_nth(-1111)