From 22e7f7f147b4fcd0e142d135aa35bb988aba54d4 Mon Sep 17 00:00:00 2001
From: Ivan Kuzaev <ivkuzaev@mail.ru>
Date: Sun, 3 Feb 2019 08:50:02 +0300
Subject: [PATCH] Update PalindromicPrime.java

Method prime(num) uses only odd numbers from 3 to square root of num as divisors.
In method functioning(y) we iterate over odd numbers as all even numbers (except of 2) are not prime.
In method functioning(y) we check at first if the number is palindrome and then if it's prime, so we don't have to call the heavy prime() method for every number.
The speed of searching palindromic primes is significantly increased.
---
 Misc/PalindromicPrime.java | 39 ++++++++++++++++++++------------------
 1 file changed, 21 insertions(+), 18 deletions(-)

diff --git a/Misc/PalindromicPrime.java b/Misc/PalindromicPrime.java
index 866467206..bb2c82480 100644
--- a/Misc/PalindromicPrime.java
+++ b/Misc/PalindromicPrime.java
@@ -1,15 +1,16 @@
 import java.util.Scanner;
+
 public class PalindromePrime {
 
     public static void main(String[] args) { // Main funtion
         Scanner in = new Scanner(System.in);
         System.out.println("Enter the quantity of First Palindromic Primes you want");
-        int n = in.nextInt(); // Input of how mant first pallindromic prime we want
-        funtioning(n); // calling funtion - functioning  
+        int n = in.nextInt(); // Input of how many first pallindromic prime we want
+        functioning(n); // calling function - functioning  
     }
 
     public static boolean prime(int num) { // checking if number is prime or not
-        for (int divisor = 2; divisor <= num / 2; divisor++) {
+        for (int divisor = 3; divisor <= Math.sqrt(num); divisor += 2) {
             if (num % divisor == 0) {
                 return false; //  false if not prime
             }
@@ -17,25 +18,27 @@ public class PalindromePrime {
         return true; // True if prime
     }
 
-    public static int reverse(int n){ //  Returns  the reverse of the number
+    public static int reverse(int n) { //  Returns  the reverse of the number
         int reverse = 0;
-        while(n!=0){
-            reverse = reverse * 10;
-            reverse = reverse + n%10;
-            n = n/10;
+        while(n != 0) {
+            reverse *= 10;
+            reverse += n%10;
+            n /= 10;
         }
         return reverse;
     }
 
-    public static void funtioning(int y){
-            int count =0;
-            int num = 2;
-            while(count < y){
-                if(prime(num) && num == reverse(num)){ // number is prime and it's reverse is same
-                    count++; // counts check when to terminate while loop
-                    System.out.print(num + "\n"); // Print the Palindromic Prime
-                }
-                num++; // inrease iterator value by one
+    public static void functioning(int y) {
+        if (y == 0) return;
+        System.out.print(2 + "\n"); // print the first Palindromic Prime
+        int count = 1;
+        int num = 3;
+        while(count < y) {
+            if(num == reverse(num) && prime(num)) { // number is prime and it's reverse is same
+                count++; // counts check when to terminate while loop
+                System.out.print(num + "\n"); // print the Palindromic Prime
             }
+            num += 2; // inrease iterator value by two
+        }
     }
-};
+}