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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.

Cubic Field Extensions

Tables and results on cubic number fields by Daniel A. Mayer.

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 represents a 99 % confidence level.

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.

Fermat Near-misses

Noam Elkies. Approximate solutions in integers.

The First 100,000 Prime Numbers

A Project Gutenberg etext.

The First 498 Bernoulli Numbers

A Project Gutenberg etext.

Imaginary Quadratic Fields

Tables of the fields with class number at most 23.

The Mathematical Foundation: Publications

Primes and various other tables available on DVD or CD. Free copies available for donation to some institutions.

Number Fields with Prescribed Ramification

Number fields of degree up to seven ramified at only a few small primes.

The Positive Integers

Information about the positive integers, with counts of some number-theoretic functions, maintained by Saqib Kadri.

Practical Numbers

A number is practical if all smaller numbers are sums of distinct divisors. Tables compiled by Giuseppe 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.

Tables and Computations

Browsable interfaces to tables and computations on elliptic curves, quadratic forms, and modular forms.

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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October 1, 2015 at 11:54:07 UTC
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