Algorithmic Number Theory: Tables and Links
Compiled by Noam Elkies. |
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. |
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 si |
Dedekind Zeta Functions
Tabulated by Eyal Goren using Pari. |
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]. |
Fermat Quotients Divisible by p
Wilfrid Keller and Jörg Richstein. A complete list of solutions (a, p) for odd prime bases a < 1000 and primes p < 10^11: for the single base a = 5 the larger interval p < 2^38. |
Genus-2 Curves with Small Odd Discriminant
FTP site by Michael Stoll. |
Imaginary Quadratic Fields
Tables of the fields with class number at most 23. |
Index Form Equations and Power Integral Bases in Algebraic Number Fields
Lists of results, description of algorithms and tables of numerical data, by István Gaál. |
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 10^16. |
Table of Masses of 32-dimensional Even Unimodular Lattices
With any given root system. Oliver King. |
Tables of Primes
Primes to 19 million; twin primes to 394 million; quadruple primes to 500 million. |
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 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. |
