added some number theory algos

examples/algorithms/mersenne_primes.cc

@@ -0,0 +1,11 @@
+#ifdef __cplusplus
+#include "../../src/algorithms/number_theory/mersenne_primes.h"
+#endif
+
+int main() {
+  int64_t n = 100;
+  std::vector<int> first_10_mersenne_primes = mersenne(10000000);
+  for (auto &x : first_10_mersenne_primes) {
+    std::cout << x << " ";
+  }
+}

src/algorithms/number_theory/eratosthenes_sieve.h

@@ -0,0 +1,23 @@
+#ifndef ERATOSTHENES_SIEVE_H
+#define ERATOSTHENES_SIEVE_H
+
+#ifdef __cplusplus
+#include <assert.h>
+#include <iostream>
+#include <vector>
+#endif
+
+std::vector<bool> soe(int64_t n) {
+  assert(n != 0);
+  std::vector<bool> prime(n + 1, true);
+  for (int64_t p = 2; p * p <= n; ++p) {
+    if (prime[p]) {
+      for (int64_t i = p * p; i <= n; i += p) {
+        prime[i] = false;
+      }
+    }
+  }
+  return prime;
+}
+
+#endif

src/algorithms/number_theory/gcd.h

@@ -1,10 +1,10 @@
+#ifndef GCD_H
+#define GCD_H
+
 #ifdef __cplusplus
 #include <iostream>
 #endif
 
-#ifndef GCD_H
-#define GCD_H
-
 /*
  *binary_gcd function.
  *@param a: first element.

src/algorithms/number_theory/mersenne_primes.h

@@ -0,0 +1,27 @@
+#ifndef MERSENNE_PRIMES_H
+#define MERSENNE_PRIMES_H
+
+#ifdef __cplusplus
+#include "eratosthenes_sieve.h"
+#include <iostream>
+#endif
+
+/*
+ *mersenne function.
+ *@param n: the upper bound
+ *Returns vector<int>: the vector includes the elements "p" from m = 2^p - 1 for
+ *which p gives us a mersenne prime number.
+ */
+std::vector<int> mersenne(int64_t n) {
+  std::vector<bool> prime = soe(n);
+  std::vector<int> elements;
+  int64_t k = 2;
+  while ((1 << k) - 1 <= n) {
+    if (prime[(1 << k) - 1]) {
+      elements.push_back(k);
+    }
+    k++;
+  }
+  return elements;
+}
+#endif