working quick_pow dec_to_bin

build.sh

@@ -0,0 +1 @@
+gcc main.c -o main -std=c11 -lm && ./main

main.c

@@ -1,6 +1,98 @@
+#include <inttypes.h>
+#include <math.h>
+#include <stdbool.h>
+#include <stdint.h>
 #include <stdio.h>
+#include <stdlib.h>
+
+int *dec_to_bin(int d, int *length) {
+    int *binary_form = calloc(20, sizeof(int));
+    int index = 0;
+    while (d != 0) {
+        binary_form[index] = d % 2;
+        d /= 2;
+        index++;
+    }
+
+    *length = index;
+
+    for (int i = index; i >= 0; i--) {
+        printf("%d", binary_form[i]);
+    }
+    printf(" index: %d\n", index);
+
+    return binary_form;
+}
+
+uint64_t quick_pow(int *d_binary, int a, int n, int length) {
+    uint64_t *powed = calloc(20, sizeof(uint64_t));
+
+    powed[0] = a;
+    for (int i = 1; i <= length; i++) {
+        powed[i] = (powed[i - 1] * powed[i - 1]) % n;
+        printf("powed: %ju, index: %d; ", powed[i], (i));
+    }
+
+    // check where in the binary are ones
+    uint64_t multiplied = 1;
+    for (int i = 0; i < length; i++) {
+        if (d_binary[i] == 1) {
+            multiplied *= powed[i];
+        }
+    }
+
+    printf("\nbm quick math: %ju; %d ", multiplied, n);
+    multiplied = multiplied % n;
+    printf("quick math: %ju", multiplied);
+
+    free(powed);
+
+    return multiplied;
+}
+
+bool prime_test(uint64_t n) {
+    printf("\n\nprime test: %jd\n", n);
+    // Miller Rabin prime test
+    // choose a base: a, which should be a prime so that (n, a) = 1
+    // then do 2 rounds of tests provided the first one did not fail
+    // 1: a^d =k 1 mod n
+    // 2: a^(d * 2^r) =k n-1 mod n
+    // d = n-1 / 2^S (where S means how many time did we divide the number till we reached the first odd number)
+    // S: see above
+    // r = {0,... S-1}
+
+    int a = 2;
+    int d = n - 1;
+    int S = 0;
+    int r = S - 1; // this stores the number of elements from 0 to S-1
+
+    while (d % 2 == 0) {
+        d = floor((double)d / 2.0);
+        S++;
+        printf("%d ", d);
+    }
+    printf("S: %d", S);
+    printf("\n");
+
+    // round 1
+    // 1: a^d =k 1 mod n
+    int length;
+    int *d_binary = dec_to_bin(d, &length);
+
+    if (quick_pow(d_binary, a, n, length) == 1) {
+        free(d_binary);
+        return true;
+    }
+
+    printf("\n\n");
+    free(d_binary);
+    return false;
+}
 
 int main() {
-    printf("Hello world!");
+    prime_test(111);
+    prime_test(29);
+    prime_test(27);
+
     return 0;
 }