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Miller–Rabin primality test: Difference between revisions
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===Deterministic up to 341,550,071,728,321===
<lang c>// calcul a^n%mod
size_t power(size_t a, size_t n, size_t mod)
{
size_t power = a;
size_t result = 1;
while (n)
{
if (n & 1)
result = (result * power) % mod;
power = (power * power) % mod;
n >>= 1;
}
return result;
}
// n−1 = 2^s * d with d odd by factoring powers of 2 from n−1
bool witness(size_t n, size_t s, size_t d, size_t a)
{
size_t x = power(a, d, n);
size_t y;
while (s) {
y = (x * x) % n;
if (y == 1 && x != 1 && x != n-1)
return false;
x = y;
--s;
}
if (y != 1)
return false;
return true;
}
/*
* if n < 1,373,653, it is enough to test a = 2 and 3;
* if n < 9,080,191, it is enough to test a = 31 and 73;
* if n < 4,759,123,141, it is enough to test a = 2, 7, and 61;
* if n < 1,122,004,669,633, it is enough to test a = 2, 13, 23, and 1662803;
* if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;
* if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13;
* if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.
*/
bool is_prime_mr(size_t n)
{
if (((!(n & 1)) && n != 2 ) || (n < 2) || (n % 3 == 0 && n != 3))
return false;
if (n <= 3)
return true;
size_t d = n / 2;
size_t s = 1;
while (!(d & 1)) {
d /= 2;
++s;
}
if (n < 1373653)
return witness(n, s, d, 2) && witness(n, s, d, 3);
if (n < 9080191)
return witness(n, s, d, 31) && witness(n, s, d, 73);
if (n < 4759123141)
return witness(n, s, d, 2) && witness(n, s, d, 7) && witness(n, s, d, 61);
if (n < 1122004669633)
return witness(n, s, d, 2) && witness(n, s, d, 13) && witness(n, s, d, 23) && witness(n, s, d, 1662803);
if (n < 2152302898747)
return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11);
if (n < 3474749660383)
return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13);
return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13) && witness(n, s, d, 17);
}</lang c>
Inspiration from http://stackoverflow.com/questions/4424374/determining-if-a-number-is-prime
=={{header|C sharp|C#}}==
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