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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.

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Type
Articles
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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