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

     P1   and   P2   are primes
     P1  +  2   =   P2


Task

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

(P1 < user-specified number & P2 < user-specified number).



Extension

 Find all twin prime pairs under 100000, 10000000 and 1000000000.
 What is the time complexity of the program? Are there ways to reduce computation time?


Examples

> Search Size: 100
> 8 twin prime pairs.

> Search Size: 1000
> 35 twin prime pairs.



Also see

   The OEIS entry: A001097: Twin primes. 
   The OEIS entry: A167874: The number of distinct primes < 10^n which are members of twin-prime pairs. 
   The OEIS entry: A077800: List of twin primes {p, p+2}, with repetition. 
   The OEIS entry: A007508: Number of twin prime pairs below 10^n. 


pairsOfPrimes: function [upperLim][
    count: 0
    j: 0
    k: 1
    i: 0
    while [i=<upperLim][
        i: (6 * k) - 1
        j: i + 2
        if and? [prime? i] [prime? j] [
            count: count + 1
        ]
        k: k + 1
    ]
    return count + 1
]
 
ToNum: 10
while [ToNum =< 1000000][
    x: pairsOfPrimes ToNum
    print ["From 2 to" ToNum ": there are" x "pairs of twin primes"]
    ToNum: ToNum * 10
]