The primality test is usually a power congruence to a given base that is coprime to , such as (from Fermat’s little theorem). For example, if is an odd prime, then the congruence will be true, but in reverse, can satisfy the congruence but turn out to be an odd composite number. Such pseudoprimes are then called pseudoprime to base , and in our example with , the first few are 341, 561, 645, 1105, 1387, 1729, 1905 (A001567 in Sloane’s OEIS). According to Neil Sloane, writing in the OEIS, the term “pseudoprime” is sometimes used specifically to refer to pseudoprimes to base 2. These are sometimes called Sarrus numbers.
Another kind of pseudoprimes are those in which a composite divides an element it indexes in a Fibonacci-like sequence. For example, a Perrin pseudoprime divides , where is the -th element in the Perrin sequence.
- 1 R. Crandall & C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001: 5.1
|Date of creation||2013-03-22 16:49:44|
|Last modified on||2013-03-22 16:49:44|
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