Vantieghems Theorem for Primality Test

Vantieghems Theorem is a necessary and sufficient condition for a number to be prime. It states that for a natural number n to be prime, the product of where , is congruent to . 
In other words, a number n is prime if and only if.

Examples:  

• For n = 3, final product is (2¹ - 1) * (2² - 1) = 1*3 = 3. 3 is congruent to 3 mod 7. We get 3 mod 7 from expression 3 * (mod (2³ - 1)), therefore 3 is prime.
• For n = 5, final product is 1*3*7*15 = 315. 315 is congruent to 5(mod 31), therefore 5 is prime.
• For n = 7, final product is 1*3*7*15*31*63 = 615195. 615195 is congruent to 7(mod 127), therefore 7 is prime.
• For n = 4, final product 1*3*7 = 21. 21 is not congruent to 4(mod 15), therefore 4 is composite.

Another way to state above theorem is, if divides , then n is prime. 
 

2 is prime
3 is prime
5 is prime
7 is prime

Time Complexity : O(limit)
Auxiliary Space: O(1)

The above code does not work for values of n higher than 11. It causes overflow in prod evaluation.