A positive integer n is called prime if n > 1 and the only factors of n are 1 and n. It is known that a positive integer n > 1 is prime if n is not divisible by any prime integer mn .

The 1230th prime number is 10,007. Let t be an integer such that 2 t 100,000,000. Then t is prime if either t is equal to one of the first 1,230 prime numbers or t is not divisible by any of the first 1,230 prime numbers.

Write a program that declares an array of size 1,230 and stores the first 1,230 prime numbers in this array. The program then uses the first 1,230 prime numbers to determine if a number between 2 and 100,000,000 is prime. If a number is not prime, then output at least one of its prime factors.

USE C++

sample output

Output

Enter a value 2  t  100,000,000: 55555 55555 is not prime, (has 5 as a prime factor)