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. 


import "/math" for Int
import "/fmt" for Fmt
 
var c = Int.primeSieve(1e8-1, false)
var limit = 10
var start = 3
var twins = 0
for (i in 1..8) {
    var j = start
    while (j < limit) {
        if (!c[j] && !c[j-2]) twins = twins + 1
        j = j + 2
    }
    Fmt.print("Under $,11d there are $,7d pairs of twin primes.", limit, twins)
    start = limit + 1
    limit = limit * 10
}