*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.

**Solution:**

(1) First we find

.

, which is our new prime number.

(2) Lets find

.

, which is not a prime since

is our new prime.

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