@InProceedings{Riv90b, author = { Ronald L. Rivest }, title = { Finding Four Million Large Random Primes }, OPTurl = { http://dx.doi.org/10.1007/3-540-38424-3_45 }, doi = { 10.1007/3-540-38424-3_45 }, pages = { 625--626 }, booktitle = { Advances in Cryptology - CRYPTO '90, 10th Annual Internation Cryptology Conference }, date = { 1990 }, publisher = { Springer }, editor = { Alfred Menezes and Scott A. Vanstone }, series = { Lecture Notes in Computer Science }, volume = { 537 }, isbn = { 978-3-540-54508-8 }, organization = { IACR }, OPTyear = { 1990 }, OPTmonth = { August 11-15, }, eventdate = { 1990-08-11/1990-08-15 }, eventtitle = { CRYPTO '90 }, venue = { Santa Barbara, California }, abstract = { A number $n$ is a (base two) pseudoprime if it is composite and satisfies the identity $$ 2^{n - 1} \equiv 1\left( {\bmod n} \right). $$ (1) Every prime satisifies (1), but very few composite numbers are pseudoprimes. If pseudoprimes are very rare, then one could even find large ``industrial strength'' primes (say for cryptographic use) by simply choosing large random values for $n$ until an $n$ is found that satisfies (1). How rare are pseudoprimes? We performed an experiment that attempts to provide an answer. We also provide some references to the literature for theoretical analyses. }, }