Is Every Prime Number Defined by Its Unique Factors?

[jonroberts74]

An integer is prime if, and only if, n > 1 and for all positive integers r and s, if
n = (r)(s), then r > 1 or s > 1.

it should be if n = rs, then r great than or equal 1 or s greater than or equal 1

correct?

 

[verty]

What you want to say is that no factor is between 1 and n. If either is 1, it works.

 

[HallsofIvy]

An integer is prime if, and only if, n > 1 and for all positive integers r and s, if
n = (r)(s), then r > 1 or s > 1.

What? No! if 6= (r)(s) then either r= 3 and s= 2 or r= 2 and s= 3 or r= 1 and s= 6 or r= 6 and r= 1. "If n= (r)(s), then r> 1 or s> 1" is true for all positive integers except 1.

It should be if n = rs, then r great than or equal 1 or s greater than or equal 1

correct?

This is now true for all positive integers. What is true for prime numbers only is "If n= (r)(s) then r= 1 or s= 1."