A non-zero element of a r
A non-zero element of a ring R is one of these elements if it is not a unit, and, for any elements x and y in R, if it divides x times y, it also divides x or y. A number n is one of these numbers if and only if "n minus one factorial" is congruent to "negative one modulo n", according to Wilson's theorem. An integer raised to the power of one of these numbers and that integer are congruent modulo the exponent, according to Fermat's little theorem. When they are equal to "one less than a power of two", these numbers are named for Mersenne. These numbers can be found using the sieve of Eratosthenes. For 10 points, name these numbers divisible only by themselves and one.
A non-zero element of a ring R is one of these elements if it is not a unit, and, for any elements x and y in R, if it divides x times y, it also divides x or y. A number n is one of these numbers if and only if "n minus one factorial" is congruent to "negative one modulo n", according to Wilson's theorem.
prime numbers [or prime elements]