This problem is to help remedy the disaster of 23 of the cla

This problem is to help remedy the disaster of 2/3 of the class not knowing what a prime number is on exam II. Show that each of the following is NOT the definition of a prime number: either exhibit a prime number that fails to satisfy the stated condition, or a nonprime number that does satisfy it. (A few of the \"definitions\"are ambiguous\' just point out the ambiguity since there is nothing else you can do with them.) In all cases we assume p to be an integer. \"p is prime if for all integers q

Solution

a) 3 doesnot satisfy.

3 is a prime but 2 <3 doesnot divide 3

c) it says -1 is the only prime. 2 is a prime 2 is divisible by -2

d) 2 is a prime 2 is divisible by -2

e) 2 is a prime 2 is divisible by -2

f) same

3 doesnot satisfy.

3 is a prime but 2 <3 doesnot divide 3

g) same

3 doesnot satisfy.

3 is a prime but 2 <3 doesnot divide 3

i)

k) every number is divisible by 1 and itself . 4 is not a prime but divisible by1 and 4