Prime numbers are closed under subtraction

This is false. If we assumed the prime numbers were closed under subtraction, then the difference of any two primes would also get us a prime number.

Take the prime numbers 11 and 7. Their difference, 11 - 7, is 4, but 4 is composite, as it has 2 as a factor other than 1 and 4. All we need is this one counterexample to prove that prime numbers are not closed under subtraction.

the reason why your question keeps getting deleted because this is not a school related question : )

i will answer your question though.

i never tried church's