Their count is asymptotic to x over the natural log of x, and Goldberg's hypothesis states that every even number can be expressed as the sum of two of these.
A specific type of these entities x obey a relation in which x squared divides the x minus Legendre symbol x over fifth Fibonacci number. Another type satisfies the conditions of Wolstonholme's theorem for the fourth power, though all of them satisfy that result for the third power. If x is one of these and 2x plus 1 is also, they are named for Germain. In addition to the Wall-Sun-Sun ones, these numbers divide themselves minus one factorial plus one according to Wilson's theorem. Their count is asymptotic to x over the natural log of x, and Goldberg's hypothesis states that every even number can be expressed as the sum of two of these. Fermat and Mersenne give their names to varieties of, for 10 points, what kind of number whose only factors are one and itself?
A specific type of these entities x obey a relation in which x squared divides the x minus Legendre symbol x over fifth Fibonacci number.
 prime numbers