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What is a counterexample to the statement all prime numbers are odd?
2 is a prime number.
What do 3 5 7 11 and 13 have in common?
They are all odd, and they are all prime numbers
All prime numbers except for 2 are odd?
All of the prime numbers are odd except for two.
Is a prime number always an odd number?
Except for 2 all other prime numbers are odd. Otherwise, they would be divisible by 2 (and thus not a prime number). This does NOT mean that all odd numbers are prime, but that all prime numbers (aside from 2) are odd.
What's a counterexample to the statement that all odd numbers can be expressed as the sum of two primes?
There is a simple counterexample: the number 1:1 is an odd numberthe first prime is 2 (not 1, see below) which is bigger than 1 so 1 cannot possibly be the sum of two primes.There are plenty of other counterexamples:The sum of two odd numbers is even;All prime numbers except 2 are odd;When adding two prime numbers together, to get an odd result one of them must be even, namely 2;So any odd number that is 2 more than a composite number will not be expressible as the sum of two primes. examples: 11, 17, 23, 27, 29, 35, 37, ...Another counterexample is the number 3:3 is an odd number3 can only be made by 2 + 11 is not a prime (see below)A prime number is a number that has exactly 2 distinct (different) factors.The number 1 has only 1 distinct factor (the number 1) and so is not a prime number; the first prime number is 2.
