In mathematics, the Perrin pseudoprimes are derived from the Perrin series of numbers. Main article: History of mathematics The evolution of mathematics can be seen to be an ever increasing series of abstractions. ... In mathematics, the Perrin numbers are defined by the recurrence relation P(0) = 3, P(1) = 0, P(2) = 2, and P(n) = P(n − 2) + P(n − 3) for n > 2. ...
The Perrin series is defined by the recurrence relation Recurrent redirects here; for the meaning of recurrent in contemporary hit radio, see Recurrent rotation. ...
P(0) = 3, P(1) = 0, P(2) = 2,
and
P(n) = P(n − 2) + P(n − 3) for n > 2.
The series begins
3 0 2 3 2 5 5 7 10 12 17 22 29 39 ... .
The numbers quickly become very large.
Consider n for which n divides P(n). Those are
n = 1, 2, 3, 5, 7, 11, 13, ...
so initially 1 followed by prime numbers. It has been proved that for all primes p, p divides P(p). In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ...
The converse is not true; such composite numbersn are called Perrin pseudoprimes, and they are known to exist, the lowest being 271441. Wikipedia does not yet have an article with this exact name. ...
External links
Zentrum für Hirnforschung Institut für Medizinische Kybernetik und Artificial Intelligence
In general, an integer which has a certain property shared by all prime numbers, but is itself not prime, is called a pseudoprime for that particular property.
The smallest pseudoprime for the base 2 is 341.
Pseudoprimes to base 2 are called Poulet numbers or sometimes Sarrus numbers or Fermatians (SIDN A001567) (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001567).
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