Reference Database
(references for the Prime Pages)
The Prime Pages

Search Site

How Many?


Prime Curios!
e-mail list

Prime Lists

Submit primes
This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

Item(s) in original BibTeX format

	author={Z. Zhang},
	title={Finding strong pseudoprimes to several bases},
	abstract={Define $\psi_m$ to be the smallest strong pseudoprime to all the first $m$
		prime bases. If we know the exact value of $\psi_m$, we will have, for
		integers $n<\psi_m$, a deterministic primality testing algorithm which
		is not only easier to implement but also faster than either the Jacobi
		sum test or the elliptic curve test. Thanks to Pomerance et al.\ and Jaeschke,
		$\psi_m$ are known for $1 \leq m \leq 8$. Upper bounds for $\psi_9,\psi_{10}$
		and $\psi_{11}$ were given by Jaeschke. In this paper we tabulate all strong
		pseudoprimes (spsp's) $n<10^{24}$ to the first ten prime bases $2, 3, \cdots,
		29,$ which have the form $n=p,q$ with $p, q$ odd primes and $q-1=k(p-1),
		k=2, 3, 4.$ There are in total 44 such numbers, six of which are also spsp(31),
		and three numbers are spsp's to both bases 31 and 37. As a result the upper
		bounds for $\psi_{10}$ and $\psi_{11}$ are lowered from 28- and 29-decimal-digit
		numbers to 22-decimal-digit numbers, and a 24-decimal-digit upper bound
		for $\psi_{12}$ is obtained. The main tools used in our methods are the
		biquadratic residue characters and cubic residue characters. We propose
		necessary conditions for $n$ to be a strong pseudoprime to one or to several
		prime bases. Comparisons of effectiveness with both Jaeschke's and Arnault's
		methods are given.},
	journal= mc,
	volume= 70,
	year= 2001,

Prime Pages' Home
Another prime page by Chris K. Caldwell