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  About site: http://www.pseudoprime.com/pseudo.html

Title: Math/Number Theory/Prime Numbers/Primality Tests - Pseudoprimes/Probable Primes Papers on primality tests and Frobenius pseudoprimes by Jon Grantham.
Behaviour_of_Prime_Numbers An insight into the Goldbach Conjecture.

Christian_Goldbach Biography, with links to other Goldbach resources.

An_\"Expository_Proof\"_of_the_Goldbach_Conjecture An elementary attack on the problem of prime sums.

Goldbach_Conjecture Article from MathWorld.

The_Goldbach_Conjecture From the Primes Glossary. Historical references and links.

Goldbach_Conjecture_Research Information on research and computations on the Goldbach Conjecture. By Mark Herkommer.


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Pseudoprimes/Probable Primes

Pseudoprimes/Probable Primes

Pseudoprimes and Other Research

I now have a weblog devoted to updates on myresearch.

Recent Developments in Primality Testing

Here are slides of my talk on this subject. The talk is containedin 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 Mentions

The Spring 1997 issue of CryptoBytes, a newsletter of RSA Labs, contains an article entitled"Fast Generation of Random, Strong RSA Primes" which refers to my work. Please note that the number "1770" should be changed to "7710". There was a June 13, 1997 article in theChristian Science Monitor thatmentioned my dissertation.

Frobenius Pseudoprimes

The proliferation of probable prime tests in recent years has produceda plethora of definitions with the word "pseudoprime" in them. I introducedthe concept of Frobenius pseudoprimes in order to present a way of viewingmany of these tests as special cases of a general principle, as well as tore-formulate them in the context of finite fields. Frobenius Pseudoprimes I am happy to be able to make available my first paper on Frobeniuspseudoprimes. This will appear in Mathematics of Computation. Take yourpick of formats. pseudo1.tex (72K) pseudo1.dvi (104K) pseudo1.ps (288K) pseudo1.pdf (264K) Random Quadratic Frobenius Test I also have made available my paper on the Random Quadratic FrobeniusTest. It is an application of ideas in the first paper to produce a probableprime test that has an expected running time 3 times as long as that of theStrong Probable Prime Test, but is more than 3 times as accurate. A Probable Prime Test with High Confidence Infinitely Many Frobenius PseudoprimesThis paper shows that for any reasonable polynomial, there are infinitelycomposites which pass a given Frobenius test. In particular, this answersa 1982 conjecture of Adamsand Shanks. pseudo3.pdf

The $620 Question

Please enjoy a list of primes that Red Alford and I have computed.I strongly believe that some sub-product of these primes is a Carmichaelnumber and a Lucas pseudoprime for the Fibonacci sequence, and also is 2or 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 Dopo Le Parole aangeboden aan Dr. A. K. Lenstra, a privatelypublished volume to honor ArjenLenstra's receipt of his doctoral degree. Since this paper is not generallyavailable, Carl gave me permission to scan it in and make it available onmy web pages. dopo.tex dopo.dvi dopo.ps dopo.pdf

Carmichael Numbers

Alford, Andrew Granville,and Pomerance showed in a 1994 paper that there were infinitely many Carmichaelnumbers. Granville has made this and relatedpapers available on the web. Jon Home Links Weblog Archive Math FamilyTree Gaming E-mail
 

Papers

on

primality

tests

and

Frobenius

pseudoprimes

by

Jon

Grantham.

http://www.pseudoprime.com/pseudo.html

Pseudoprimes/Probable Primes 2009 January

dvd rental

dvd


Papers on primality tests and Frobenius pseudoprimes by Jon Grantham.

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