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import math
import random
def erathosphene(n):
is_prime = [True] * n
p = 2
while p * p < n:
cur = p * p;
while cur < n:
is_prime[cur] = False;
cur += p;
while not is_prime[p + 1]:
p += 1;
p += 1
primes = []
for i, p in enumerate(is_prime):
if p:
primes.append(i)
return primes[2:]
def fast_power(base, power):
result = 1
while power > 0:
if power % 2 == 0:
power = power // 2
base *= base
else:
power -= 1
result = result * base
power = power // 2
base *= base
return result
def get_only_prime_divisors(n):
factors = []
if (n % 2 == 0):
factors.append(2)
while (n % 2 == 0):
n = n // 2
for i in range(3, int(math.sqrt(n)) + 1, 2):
if (n % i == 0):
factors.append(i)
while (n % i == 0):
n = n // i
if (n > 2):
factors.append(n)
return factors
def pocklington_criterion(n, borded_a):
prev_n = n - 1
prime_divisors = get_only_prime_divisors(prev_n)
prime_divisors = filter(lambda q: q > math.sqrt(n) - 1, prime_divisors)
for a in range(2, borded_a):
if pow(a, prev_n, n) != 1:
continue
for q in prime_divisors:
if math.gcd(n, fast_power(a, prev_n // q) - 1) == 1:
return True
return False
def get_random_number(n):
while True:
number = random.randrange(2 ** (n-1) + 1, 2 ** n - 1)
for divisor in first_primes_list:
if number % divisor == 0 and divisor ** 2 <= number:
break
else:
return number
def create_prime(n, a):
while True:
number = get_random_number(n)
if pocklington_criterion(number, a):
return number
first_primes_list = erathosphene(500)
if __name__ == "__main__":
print("Введите количество бит генерируемого простого числа:")
n = int(input())
print("Введите верхнюю границу числа 'a' в критерии Поклингтона (не меньше 3):")
a = int(input())
result = create_prime(n, a)
print(f"Сгенерированное простое число: {result}")
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