Question
Identify whether each statement is true or false. Explain.
(a) There is no prime number whose units digit is 4.
(b) A product of primes can also be prime.
(c) Prime numbers do not have any factors.
(d) All even numbers are composite numbers.
(e) 2 is a prime and so is the next number, 3. For every other prime, the next number is composite.

Answer

(a) True.
A prime number must end in 1, 3, 7, or 9 (except for the number 2) because any number ending in 0, 2, 4, 6 or 8 is divisible by 2.
Thus, there is no prime number whose units digit is 4.
(b) False.
A product of prime numbers is only prime if it involves exactly one prime number. When you multiply two or more prime numbers together, the result is always a composite number, not a prime. As this number has 2 factors now.
(c) False.
Prime numbers have exactly two factors 1 and itself.
(d) False.
The number 2 is an even number, but it is not composite. As it is a prime number.
(e) True.
For every prime number greater than 2, the next number is composite.

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