Algorithmic Number Theory: Tables and Links
Compiled by Noam Elkies. |
Algorithms for Solving Index Form Equations and Computing Power Integral Bases
Lists of results, description of algorithms and tables of numerical data, by István Gaál. |
Bernoulli Computations
Irregular primes and relative class numbers. Irregular pairs (and Vandiver and cyclotomic residues) for primes up to 8 million. Compiled by Amin Shokrollahi. |
Carmichael and Perrin
The 150 Carmichael numbers out of 246683 up to 10^16 that are Perrin pseudoprimes. |
Carmichael Numbers and Lehmer's Problem
Carmichael numbers n up to 10^9 together with phi(n), (n-1)/phi(n) and the factorization of n. Compiled by Jan Kristian Haugland. |
Cubic Field Extensions
Tables and results on cubic number fields by Daniel A. Mayer. |
Curves of Genus 2
FTP site maintained by Victor Flynn. Formulae for Jacobian arithmetic and Maple algorithms. |
Database for Polynomials over the Rationals
By Jürgen Klüners and Gunter Malle. Polynomials for all transitive groups up to degree 15, for most of the possible combinations of signature and Galois group. Up to degree 7 the fields with minimal (absolute) discriminant with given Galois group and s |
Database of Local Fields
By John W. Jones and David P. Roberts. Tables of low degree extensions of Qp, for small p. |
Dedekind Zeta Functions
Tabulated by Eyal Goren using Pari. |
Enumeration of Twin Primes and Brun's Constant
Enumeration of the twin primes, and the sum of their reciprocals, to 1.6 × 10^15. An improved estimate is obtained for Brun's constant, B2 = 1.90216 05824 ± 0.00000 00030. Error analysis is presented to support the opinion that the stated error bound re |
Extended Counts of Twin Primes
By Thomas Nicely. Counts in decades up to 10^12 then in steps of 10^12 up to 3.10^15, giving 3,310,517,800,844 pairs. |
Factorization Tables
Tables of the factorization of sigma(n). |
Fermat Near-misses
Noam Elkies. Approximate solutions of x^n + y^n = z^n in integers with 0 < x <= y < z < 2^23 and n in [4,20]. |
Genus-2 Curves with Small Odd Discriminant
FTP site by Michael Stoll, with MAGMA code. |
Imaginary Quadratic Fields
Tables of the fields with class number at most 23. |
Multiply Perfect Numbers
Over 2000 multiperfect numbers sorted by numerical value and by factorisation. |
Number Field Tables
FTP site at the University of Bordeaux. Fields of degree up to 7. |
Number Fields with Prescribed Ramification
Number fields of degree up to seven ramified at only a few small primes. |
Practical Numbers
A number is practical if all smaller numbers are sums of distinct divisors. Tables compiled by Guiseppe Melfi. |
Pseudoprimes and Carmichael Numbers
Tables of the Fermat pseudoprimes base 2 up to 10^13 and Carmichael numbers up to 10^17 compiled by Richard Pinch. |
Table of Masses of 32-dimensional Even Unimodular Lattices
With any given root system. Oliver King. |
Tables and Computations
Browsable interfaces to tables and computations on elliptic curves, quadratic forms, and modular forms. |
Tables of Number Fields
Hilbert class field of totally real fields of degree 2, 3 and 4; Totally real fields with small root discriminant; Totally real quintic dihedral fields. By Xavier-François Roblot. |
Tables of Primes
Various tables available on DVD or CD. Free copies available for donation to some institutions. |
The First 100,000 Prime Numbers
A Project Gutenberg etext. |
The First 28,915 Odd Primes
Tabulated using a simple C program. |
The First 498 Bernoulli Numbers
A Project Gutenberg etext. |
The Positive Integers
Information about the positive integers, with counts of some number-theoretic functions, maintained by Saqib Kadri. |
The Value of Zeta(3) to 1,000,000 Decimal Digits
A Project Gutenberg etext. |
Vanishing Fermat Quotients
R. Ernvall and T. Metsänkylä. Tables of the pairs (p,k) such that the Fermat quotient q(k) = (k^{p-1}-1)/p vanishes mod p. The tables cover the primes p up to one million and, for each prime, the range 1 < k < p. |
Zeroes of the Riemann Zeta Function
By Andrew Odlyzko. The first 100,000 to 8 places, the first 1000 to 1000 places. |
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