The twin prime calculator is a pattern that was constructed by Dean Hickerson on September 9, 1994 that produces a stream of lightweight spaceships representing twin prime numbers (except for the pair (3, 5)). In particular, N and N+2 are both prime if and only if a lightweight spaceship escapes past the gun at the bottom-left corner at about generation 120N+540. It works by attaching a period 240 glider gun to the bottom-left corner of Hickerson's original prime number calculator, primer, which allows a lightweight spaceship to pass by it if and only if another lightweight spaceship tried to pass by 240 generations earlier.
By having various guns pointed at the output stream of of primer, it is possible to similarly construct various other prime-generating patterns. For example, a prime quadruplet calculator and a cousin prime calculator have both been constructed.