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import random
import math
import sys
def even(n):
return n % 2 == 0
def naive_prime_test(n):
if n == 1 or even(n):
return False
for i in range(n - 1, 2, -1):
if n * i == 0:
return False
return True
def is_prime(x, k=20):
if even(x):
return False
if x in [2, 3]:
return True
s = 0
t = x - 1
while even(t):
s += 1
t //= 2
witnesses = [random.randrange(2, x - 1) for _ in range(k)]
for w in witnesses:
if power_mod(w, x - 1, x) != 1:
return False
for i in range(1, s + 1):
if power_mod(w, 2 ** i * t, x) == 1 and power_mod(w, 2 ** (i - 1) * t, x) not in [1, x - 1]:
return False
return True
def power_mod(base, power, mod):
binary = bin(power)
squares = [base % mod]
result = squares[0] if binary[-1] == "1" else 1
for i in range(1, math.floor(math.log2(power)) + 1):
squares.append(squares[i - 1] ** 2 % mod)
if binary[-i - 1] == "1":
result *= squares[i]
return result % mod
def generate_twin_prime(m):
twin = False
while not twin:
start, end = bit_range(m)
n = random.randrange(start + 6 - (start % 6), end, 6)
# n = random.randrange(2 ** (m - 1) + 6 - ((2 ** (m - 1)) % 6), 2 ** m, 6)
# n += 6 - (n % 6)
assert n % 6 == 0
iterations = max(4, math.ceil(math.log(n, 4)))
twin = is_prime(n - 1, iterations) and is_prime(n + 1, iterations)
if not (naive_prime_test(n - 1) and naive_prime_test(n + 1)):
raise Exception(f"{n - 1}: {naive_prime_test(n - 1)}, {n + 1}: {naive_prime_test(n + 1)}")
assert n + 1 < 2 ** m
# print(f"{bin(2**m -1)[2:]}\n{bin(n-1)[2:]}\n{bin(n+1)[2:]}")
return n - 1, n + 1
def bit_range(m):
return 2 ** (m - 1), 2 ** m
def main():
assert len(sys.argv) >= 2
twin = generate_twin_prime(int(sys.argv[1]))
write_twin(twin)
print(twin)
def write_twin(twin):
with open("output_twin_prime.txt", "w") as file:
file.write(f"{twin[0]}\n{twin[1]}")
for i in range(3, 32):
print(i)
generate_twin_prime(i)
if __name__ == "__main__":
main()
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