Prime (#585)

* Prime

Here we can check prime upto 10^8 in O(1). It is very useful in Competitive programming.

* Update and rename Math/Primeupto10^8.cpp to math/primes_up_to_10^8.cpp

* long long -> int64

* cstdint::int64_t

* int64_t

* std::cin

math/primes_up_to_10^8.cpp

@@ -0,0 +1,27 @@
+#include<iostream>
+#include <cstring>
+
+char prime[100000000];
+
+void Sieve(int64_t n) {
+    memset(prime, '1', sizeof(prime));  // intitize '1' to every index
+    prime[0] = '0';  // 0 is not prime
+    prime[1] = '0';  // 1 is not prime
+    for (int p = 2; p * p <= n; p++) {
+        if (prime[p] == '1') {
+            for (int i = p * p; i <= n; i += p)
+                prime[i] = '0';  // set all multiples of p to false
+        }
+    }
+}
+
+
+int main() {
+    Sieve(100000000);
+    int64_t n;
+    std::cin >> n;  // 10006187
+    if (prime[n] == '1')
+        std::cout << "YES\n";
+    else
+        std::cout << "NO\n";
+}