Twin primes

Twin primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Twin primes are pairs of natural numbers   (P₁  and  P₂)   that satisfy the following:

1.     P₁   and   P₂   are primes
2.     P₁  +  2   =   P₂

Task

Write a program that displays the number of twin primes that can be found under a user-inputted number.

Examples

> Search Size: 100
> 8 twin prime pairs.

> Search Size: 1000
> 35 twin prime pairs.

Java

BigInteger Implementation: <lang Java> import java.math.BigInteger; import java.util.Scanner;

public class twinPrimes {

   public static void main(String[] args) {
       Scanner input = new Scanner(System.in);
       System.out.println("Search Size: ");
       BigInteger max = input.nextBigInteger();
       int counter = 0;
       for(BigInteger x = new BigInteger("3"); x.compareTo(max) <= 0; x = x.add(BigInteger.ONE)){
           BigInteger sqrtNum = x.sqrt().add(BigInteger.ONE);
           if(x.add(BigInteger.TWO).compareTo(max) <= 0) {
               counter += findPrime(x.add(BigInteger.TWO), x.add(BigInteger.TWO).sqrt().add(BigInteger.ONE)) && findPrime(x, sqrtNum) ? 1 : 0;
           }
       }
       System.out.println(counter + " twin prime pairs.");
   }
   public static boolean findPrime(BigInteger x, BigInteger sqrtNum){
       for(BigInteger divisor = BigInteger.TWO; divisor.compareTo(sqrtNum) <= 0; divisor = divisor.add(BigInteger.ONE)){
           if(x.remainder(divisor).compareTo(BigInteger.ZERO) == 0){
               return false;
           }
       }
       return true;
   }

} </lang>

Output:

> Search Size: 
> 100
> 8 twin prime pairs.

> Search Size: 
> 1000
> 35 twin prime pairs.

REXX

<lang rexx>/*REXX program counts the number of twin primes under a specified number N (or a list).*/ parse arg $ . /*get optional number of primes to find*/ if $= | $="," then $= 100 1000 10000 100000 /*Not specified? Then assume default.*/ w= length( word($, words($) ) ) /*get length of the last number in list*/

      do i=1  for words($);       x= word($, i) /*process each N─limit in the  $  list.*/
      say right( genP(x), 20)   ' twin primes found under '   right(x, max(length(x), w))
      end   /*i*/

exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: arg y; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; #= 5; tp= 3; s= @.# + 2

           do j=s  by 2  while  j<y             /*continue on with the next odd prime. */
           parse var  j    -1  _              /*obtain the last digit of the  J  var.*/
           if _      ==5  then iterate          /*is this integer a multiple of five?  */
           if j // 3 ==0  then iterate          /* "   "     "    "     "     " three? */
           if j // 7 ==0  then iterate          /* "   "     "    "     "     " seven? */
           if j //11 ==0  then iterate          /* "   "     "    "     "     " eleven?*/
                                                /* [↓]  divide by the primes.   ___    */
                 do k=6  to #  while  k*k<=j    /*divide  J  by other primes ≤ √ J     */
                 if j//@.k == 0  then iterate j /*÷ by prev. prime?  ¬prime     ___    */
                 end   /*k*/                    /* [↑]   only divide up to     √ J     */
           #= #+1                               /*bump the count of number of primes.  */
           @.#= j;            _= # - 1          /*define J prime; point to prev. prime.*/
           if j-2==@._  then tp= tp + 2         /*This & previous prime twins?  Bump tp*/
           end   /*j*/
    return tp</lang>

output   when using the default inputs:

                  15  twin primes found under     100
                  69  twin primes found under    1000
                 409  twin primes found under   10000
                2447  twin primes found under  100000