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# Program to search p, q primes so that # q = (p**3-p-13)/(109*(3*p+64)) # Python3 programs to do Miller-Rabin primality test P=15000 import random def power(x, y, p): res = 1 x = x % p while (y > 0): if (y & 1): res = (res * x) % p y = y>>1; # y = y/2 x = (x * x) % p return res def miillerTest(d, n): a = 2 + random.randint(1, n - 4) x = power(a, d, n) if (x == 1 or x == n - 1): return True; while (d != n - 1): x = (x * x) % n d *= 2 if (x == 1): return False if (x == n - 1): return True return False. def prime( n, k): if (n <= 1 or n == 4): return False; if (n <= 3): return True d = n - 1; while (d % 2 == 0): d //= 2 for i in range(k): if (miillerTest(d, n) == False): return False return True # Driver Code # Number of iterations k = 4 for p in range(2,P): if((p**3-p-13)%(109*(3*p+64))==0): if(prime(p,k) and prime((p**3-p-13)//(109*(3*p+64)),k)): print(p,(p**3-p-13)//(109*(3*p+64)))
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