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. 


ClearAll[TwinPrimeCount]
TwinPrimeCount[mx_] := Module[{pmax, min, max, total},
  pmax = PrimePi[mx];
  total = 0;
  Do[
   min = 10^6 i;
   min = Max[min, 1];
   max = 10^6 (i + 1);
   max = Min[max, pmax];
   total += Count[Differences[Prime[Range[min, max]]], 2]
   ,
   {i, 0, Ceiling[pmax/10^6]}
   ];
  total
 ]
Do[Print[{10^i, TwinPrimeCount[10^i]}], {i, 9}]