The VincS theorem states that the primorial (see note) of any natural number n (≥ 2) contains inside itself the information to determine if the natural number immediately greater x (= n +1) is a prime number or not. The theorem was born by reading about the Wilson's primality test and by the inner faith that there should be a way to achieve the same result without using the huge factorial necessary to perform the test.

Cornerstone of the work is the Euclid's theorem on the gcd of which we will provide an original demonstration applied to the primorial.

The VincS primality test (derived from the theorem) can shrink, inside the primorial, the number to carry on for testing. To tell the truth, the Wilson's test has the advantage that it doesn't need to know all the prime numbers less than the number we want to test. On the other hand, the VincS test behaves almost like a sieve (like the Eratosthenes one) but it has the advantage of opening the way to new scenarios for which I will tell you if you continue to follow me.

Further details on:
www.vincs.it