# Numbers, Constants and Computation

Written by: Xavier Gourdon and Pascal Seba

Two Frenchman working as computer scientists in numerical analysis, Xavier Gourdon and Pascal Sebah have created this great informational site dedicated to mathematical, algorithmic and historical aspects of some classical mathematical concepts. Several programs are offered for downloading and everything comes with easy to understand explanations.

## Numbers, Constants and Computation Index

Mathematical constants
Archimedes’ constant p
The constant e
The logarithmic constant log 2
Pythagoras’ constant Ö2
Euler’s constant g
Apery’s constant z(3)
Table of Digits with 50 decimal places
Records of computation
Algorithms
Arbitrary precision computation
FFT based multiplication of large numbers
Binary splitting method
Computation of inverse and square root in high precision
Newton’s iteration
Acceleration of the convergence of series: Some techniques to accelerate the convergence of series. Also includes a recent general and powerful technique to accelerate the convergence of alternating series.
N-th digit computation: How to compute directly the n-th digit of p, log 2, ¼. Includes a new algorithm to compute directly the n-th decimal digit of p.
Programs
PiFast
Easy programs for constants computation
Tiny programs for constants computation
Online computation of some constants
Number theory
Counting primes
Contribute to the pi(x) table project: A new distributed computation to construct a table of large values of pi(x)
The pi(x) project
Twin primes and Brun’s constant
Compute the number of primes on line
Some constants from Number Theory
Miscellaneous
Classification of numbers (irrational, transcendental, ¼)
Irrationality proofs: Some proofs of the irrationality of p, e and log 2.
The Gamma function
The Riemann Zeta function Includes details about the latest numerical Riemann Hypothesis verification record (on the first ten trillion-th zeros) and zeros computations at very large height.
Bernoulli numbers
Mathematical quotes
References

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Numbers, Constants and Computation