Quandaries and Queries

Name: Julie

#1. Suppose you are given a number (n) and told that 1 and the number (n) divide into (n). Does that mean (n) is prime?

#2. Suppose that p is a prime number greater than or equal to 3. Show that p+1 cannot be a prime number.

Hi Julie,

For every number n, 1 and n divide n. What makes primes special is that only 1 and n divide n if n is a prime. So, for example if n=6 then 1 and 6 divide 6 but so do 2 and 3. Hence 6 is not a prime. On the other hand if n=7 then 1 and 7 divide 7 but no other positive integer divides 7. Thus 7 is a prime.

Suppose than n is an even number, larger than or equal to 3. Can n be a prime? No it can't because 1 and n divide n but so does 2 since n is even. Thus if p is a prime and p is greater than or equal to 3 then p is odd. So what do you know about p+1?


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