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Finding pseudoprimes

Published online by Cambridge University Press:  23 January 2015

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail:, g.jameson@lancaster.ac.uk
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Extract

Recall that Fermat's ‘little theorem’ says that if p is prime and a is not a multiple of p, then ap − 1 ≡ 1 mod p.

This theorem gives a possible way to detect primes, or more exactly, non-primes: if for a certain a coprime to n, a− 1 is not congruent to 1 mod n, then, by the theorem, n is not prime. A lot of composite numbers can indeed be detected by this test, but there are some that evade it. Let us give ourselves some notation and terminology to discuss them.

Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 534 , November 2011 , pp. 420 - 432
Copyright
Copyright © The Mathematical Association 2011

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References

1. Jameson, G. J. O., Finding Carmichael numbers, Math. Gaz., 95 (July 2011) pp. 244–255.Google Scholar
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7. Jameson, G. J. O., Carmichael numbers and pseudoprimes, at http://www.maths.lancs.ac.uk/~jamesonGoogle Scholar