As has been pointed out, Z/256Z has zero-divisors, so it's not a field.
"Powers of primes are also fields" doesn't mean anything; integers are integers, not fields. "Powers of primes are orders of finite fields" is correct; so there is a field of order 256, but it's not Z/256Z. (Rather, you get it by finding a degree-8 irreducible polynomial over Z/2Z, and adjoining a root of it. In fact, the article gives the specific polynomial x^8 + x^4 + x^3 + x + 1.)
Comments
No, this is incorrect.
As has been pointed out, Z/256Z has zero-divisors, so it's not a field.
"Powers of primes are also fields" doesn't mean anything; integers are integers, not fields. "Powers of primes are orders of finite fields" is correct; so there is a field of order 256, but it's not Z/256Z. (Rather, you get it by finding a degree-8 irreducible polynomial over Z/2Z, and adjoining a root of it. In fact, the article gives the specific polynomial x^8 + x^4 + x^3 + x + 1.)