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.

Step-by-step 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.

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316