## Pseudoprimes/Probable Primes## Pseudoprimes and Other ResearchI now have a weblog devoted to updates on my research. ## Recent Developments in Primality TestingHere are slides of my talk on this subject. The talk is contained in two separate files. - talk0797.tex(16K)
- talk0797.dvi(20K)
- talk0797.ps (152K)
- talk0797.pdf (244K)
- talk0797a.tex(4K)
- talk0797a.dvi(4K)
- talk0797a.ps (50K)
- talk0797a.pdf (60K)
## Media MentionsThe Spring 1997 issue of There was a June 13, 1997 article in the ## Frobenius PseudoprimesThe proliferation of probable prime tests in recent years has produced a plethora of definitions with the word "pseudoprime" in them. I introduced the concept of Frobenius pseudoprimes in order to present a way of viewing many of these tests as special cases of a general principle, as well as to re-formulate them in the context of finite fields. ## Frobenius PseudoprimesI am happy to be able to make available my first paper on Frobenius pseudoprimes. This will appear in Mathematics of Computation. Take your pick of formats. - pseudo1.tex (72K)
- pseudo1.dvi (104K)
- pseudo1.ps (288K)
- pseudo1.pdf (264K)
## Random Quadratic Frobenius TestI also have made available my paper on the Random Quadratic Frobenius Test. It is an application of ideas in the first paper to produce a probable prime test that has an expected running time 3 times as long as that of the Strong Probable Prime Test, but is more than 3 times as accurate. ## Infinitely Many Frobenius PseudoprimesThis paper shows that for any reasonable polynomial, there are infinitely composites which pass a given Frobenius test. In particular, this answers a 1982 conjecture of Adams and Shanks.## The $620 QuestionPlease enjoy a list of primes that Red Alford and I have computed. I strongly believe that some sub-product of these primes is a Carmichael number and a Lucas pseudoprime for the Fibonacci sequence, and also is 2 or 3 mod 5. This would be worth $620, so if you can assist in any way, I can make it worth your while. These computations are based on a heuristic given in 1984 by Carl Pomerance. The paper "appeared"
in ## Carmichael NumbersAlford, Andrew Granville, and Pomerance showed in a 1994 paper that there were infinitely many Carmichael numbers. Granville has made this and related papers available on the web. |
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