Question

1.28. Let {p1, p2,...,pr} be a set of prime numbers, and let N = p1p2 ··· pr + 1. Prove that N is divisible by some prime not in the original set.Hoffstein, Jeffrey. An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) (p. 54). Springer New York. Kindle Edition.

Answer 1

Explanation:

Let N = {P1, P2, ....Pr +1}

This implies that if N is a prime, using mod1, then N is not divisible by P since we are aware that for every integer, it must be easy to factor them into product of prime. so we say, if N is not prime, there is a high probability that it will still be divisible by some prime and not all primes, as such the p value is not among the element listed in the bracket.

In the N = {P1, P2, ....Pr +1}, they are all exact number that are divisible by some prime but not in among the elements listed in he bracket, most possible there are infinitely many prime numbers.