Adleman-Pomerance-Rumely primality test

The Adleman-Pomerance-Rumely primality test, often shortened to APR, is an algorithm for deciding whether a number is prime. Unlike other and faster tests used for the same purpose, it uses no random numbers, which makes it a deterministic primality test. It is named after its discoverers Leonard Adleman, Carl Pomerance and Robert Rumely, who described it in a 1983 paper in the Annals of Mathematics, and the test works with arithmetic in cyclotomic fields. Henri Cohen and Hendrik Willem Lenstra later improved it in a version commonly called APR-CL, which can test an integer n in time (log n) raised to a power that is O of log log log n, a bound that grows only slightly faster than polynomial. Implementations include UBASIC under the name APRT-CLE, the Pari/GP isprime function, which uses APR-CL under certain conditions, the open source mpz_aprcl library and Jean Penné's LLR program.