How to resolve the algorithm Miller–Rabin primality test step by step in the bc programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Miller–Rabin primality test step by step in the bc programming language
Table of Contents
Problem Statement
The Miller–Rabin primality test or Rabin–Miller primality test is a primality test: an algorithm which determines whether a given number is prime or not. The algorithm, as modified by Michael O. Rabin to avoid the generalized Riemann hypothesis, is a probabilistic algorithm. The pseudocode, from Wikipedia is:
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Step by Step solution about How to resolve the algorithm Miller–Rabin primality test step by step in the bc programming language
Source code in the bc programming language
seed = 1 /* seed of the random number generator */
scale = 0
/* Random number from 0 to 32767. */
define rand() {
/* Cheap formula (from POSIX) for random numbers of low quality. */
seed = (seed * 1103515245 + 12345) % 4294967296
return ((seed / 65536) % 32768)
}
/* Random number in range [from, to]. */
define rangerand(from, to) {
auto b, h, i, m, n, r
m = to - from + 1
h = length(m) / 2 + 1 /* want h iterations of rand() % 100 */
b = 100 ^ h % m /* want n >= b */
while (1) {
n = 0 /* pick n in range [b, 100 ^ h) */
for (i = h; i > 0; i--) {
r = rand()
while (r < 68) { r = rand(); } /* loop if the modulo bias */
n = (n * 100) + (r % 100) /* append 2 digits to n */
}
if (n >= b) { break; } /* break unless the modulo bias */
}
return (from + (n % m))
}
/* n is probably prime? */
define miller_rabin_test(n, k) {
auto d, r, a, x, s
if (n <= 3) { return (1); }
if ((n % 2) == 0) { return (0); }
/* find s and d so that d * 2^s = n - 1 */
d = n - 1
s = 0
while((d % 2) == 0) {
d /= 2
s += 1
}
while (k-- > 0) {
a = rangerand(2, n - 2)
x = (a ^ d) % n
if (x != 1) {
for (r = 0; r < s; r++) {
if (x == (n - 1)) { break; }
x = (x * x) % n
}
if (x != (n - 1)) {
return (0)
}
}
}
return (1)
}
for (i = 1; i < 1000; i++) {
if (miller_rabin_test(i, 10) == 1) {
i
}
}
quit
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