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The Lucas–Lehmer test works as follows. Let M p = 2 p − 1 be the Mersenne number to test with p an odd prime. The primality of p can be efficiently checked with a simple algorithm like trial division since p is exponentially smaller than M p. Define a sequence {} for all i ≥ 0 by
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
Aliquot sequence and Aliquot sum dynamics Abundant number; Almost perfect number; Amicable number; Betrothed numbers; Deficient number; Quasiperfect number; Perfect number; Sociable number; Collatz conjecture; Digit sum dynamics Additive persistence; Digital root; Digit product dynamics Multiplicative digital root; Multiplicative persistence ...
A randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described as random (patternless). In stochastic modeling , as in some computer simulations , the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to ...
The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. It relies on bounding sums of terms in the series. This convergence criterion is named after Augustin-Louis Cauchy who published it in his textbook Cours d'Analyse 1821.
The serial test, did the same thing but for sequences of two digits at a time (00, 01, 02, etc.), comparing their observed frequencies with their hypothetical predictions were they equally distributed. The poker test, tested for certain sequences of five numbers at a time (AAAAA, AAAAB, AAABB, etc.) based on hands in the game poker.
A digit-span task is used to measure working memory's number storage capacity. Participants see or hear a sequence of numerical digits and are tasked to recall the sequence correctly, with increasingly longer sequences being tested in each trial. The participant's span is the longest number of sequential digits that can accurately be remembered.
The tests are the monobit test (equal numbers of ones and zeros in the sequence), poker test (a special instance of the chi-squared test), runs test (counts the frequency of runs of various lengths), longruns test (checks whether there exists any run of length 34 or greater in 20 000 bits of the sequence)—both from BSI [21] and NIST, [22] and ...