Solutions to Exercises in the Introduction of How To Prove It by Daniel J Velleman.
Problem (3): The proof of Theorem 3 gives a method for finding a prime number different from any in a given list of prime numbers.
(a) Use this method to find a prime different from 2, 3, 5, 7.
(b) Use this method to find a prime different from 2, 5, 11.
(1) First we find
, which is our new prime number.
(2) Lets find
, which is not a prime since
is our new prime.