Exists a prime number greater than n

Reference no: EM13712643

Consider the proof of the following.

Statement: Let n be a positive integer. There exists a prime number greater than n .

Proof: Consider m = n ! + 1. We know that m is divisible by some prime p . But no number between 2 and
n is a divisor of m. It follows that p>n

(a) Use (Strong) Mathematical Induction to prove that every integer greater than 2 is either prime or a product of primes.
(b) Why isn't m divisible by any number between 2 and n?
(c) A consequence of the Statement is that there are an innite number of primes.

Reference no: EM13712643

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