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. 


func twin_primes_count(upto) {
    var count = 0
    var p1 = 2
    each_prime(3, upto, {|p2|
        if (p2 - p1 == 2) {
            ++count
        }
        p1 = p2
    })
    return count
}
 
for n in (1..9) {
    var count = twin_primes_count(10**n)
    say "There are #{count} twin primes <= 10^#{n}"
}