For 10 points, name these numbers whose only factors are one and themselves.
A sequence of numbers with this property contains arbitrarily long arithmetic progressions by the Green-Tao theorem. If x is has this property and 2 x plus 1 also has this property, then the resultant values are named for Germain. Carmichael numbers do not have this property even though they pass the Fermat test. Goldbach's conjecture states that every even integer can be represented as the sum of two numbers with this property. For 10 points, name these numbers whose only factors are one and themselves.
A sequence of numbers with this property contains arbitrarily long arithmetic progressions by the Green-Tao theorem.
primality [or prime numbers; accept word forms]