The Green-Tao Theorem proved that the sequence of these numbers contained arbitrarily long arithmetic progressions. The Sophie-Germain variety of these is such that both x and 2x+1 are these kind of numbers. Wilson's Theorem states that (n-1)! is congruent to -1 mod n whenever n is this kind of number. The Mersenne variety of these are of the form 2^n - 1, where n itself is also one of these. There is notably only one even example of these; the rest are odd. For 10 points, name these numbers, examples of which include 37, 17, 7, and 2.
The Green-Tao Theorem proved that the sequence of these numbers contained arbitrarily long arithmetic progressions. The Sophie-Germain variety of these is such that both x and 2x+1 are these kind of numbers. Wilson's Theorem states that (n-1)! is congruent to -1 mod n whenever n is this kind of number. The Mersenne variety of these are of the form 2^n - 1, where n itself is also one of these. There is notably only one even example of these; the rest are odd. For 10 points, name these numbers, examples of which include 37, 17, 7, and 2.
The Green-Tao Theorem proved that the sequence of these numbers contained arbitrarily long arithmetic progressions.