APR Priority Test

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APR Priority Test - an algorithm created in the early 1980s by Leonard Adleman, Carl Pomerance, and Robert Rumely to prove that a given natural number is prime. In practice, the algorithm was able to verify the primeval of numbers with several thousand decimal digits. The time complexity of the algorithm (the so-called Cohen-Lenstry variant) is: O ( ( log n ) log log log n ) {\displaystyle \mathrm {O} ((\log \,n)^{\log \,\log \,\log \,n})} ,

where n is the number to check for prime. It is almost polynomially dependent on the length of the number.

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