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. 


using Formatting, Primes
 
function counttwinprimepairsbetween(n1, n2)
    npairs, t = 0, nextprime(n1)
    while t < n2
        p = nextprime(t + 1)
        if p - t == 2
            npairs += 1
        end
        t = p
    end
    return npairs
end
 
for t2 in (10).^collect(2:8)
    paircount = counttwinprimepairsbetween(1, t2)
    println("Under", lpad(format(t2, commas=true), 12), " there are",
        lpad(format(paircount, commas=true), 8), " pairs of twin primes.")
end
 