Tutorial for Assignment 1. Introduction to Mathematical Thinking.

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:Arial;color:#000000;} .ft02{font-size:18px;font-family:Arial;color:#000000;} .ft03{font-size:18px;font-family:CambriaMath;color:#000000;} .ft04{font-size:18px;font-family:ArialMT;color:#000000;} .ft05{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Introduction to Mathematical Thinking. Tutorial for Assignment 1 QUESTION. To show that the number N=(P , ……, P )+1 is not always prime (where P 1 𝑛 1 ….. P are the first n primes ) , find an n for which (P ….. P )+1 is not prime. 𝑛 1 𝑛 (2*3)+1=7 (2*3*5)+1=31 (2*3*5*7)+1=211 (2*3*5*7*11*13)+1 = 30,031=59*509 ( not prime) Question is related to Euclid's proof that there are infinitely many primes. One crucial pointin that proof, we looked at the number p1 through pn which enumerates the first n primesand multiply them together and add 1. Also proof mentioned that this number is not always prime. Question 8 asks how you would prove that it is not always prime. The answer is by findinga number, n, such that when you multiply the first n primes and add 1, it is not prime. One way to do this would be to look at the first two prime numbers and multiply themtogether, then add 1. The result, 7, is a prime. Try another one: (2 x 3 x 5) + 1 = 31. That'salso prime. Let us try another. (2 x 3 x 5 x 7) + 1 = 211, which is a prime. You may be losing heart bynow, but if you continue the pattern with the primes 2, 3, 5, 7, 11, 13 and add 1: 2 + (3 x 5x 7) + 1 = 30,031 and this is not prime since it is divisible by 59 and 509. So here we have an example of a number that is not prime. In order to show that not everynumber of this form is prime, all you have to do is find one single example of a number inthis form which is not prime. And we've done it. This is the answer to question; this is how we prove that these numbers are not alwaysprime.