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. 


  [ dup dip
      [ eratosthenes
        0 1 primes share ]
    bit 1 - & 1 >>
    [ dup while
      dup 5 & 5 = if
        [ rot 1+ unrot ]
      2 >>
      dip [ 2 + ]
      again ]
    2drop ]                is twinprimes ( n --> [ )
 
  5 times
    [ say "Number of twin primes below "
      10 i^ 1+ ** dup echo
      say " is "
      twinprimes echo say "." cr ]