Monthly Archives: September 2012

On the numerical evaluation of factorials III

Sieving Primes

The fastest know algorithm to compute factorials uses the prime factors of the factorial. This can be done quite easily but needs a list of primes to do so. One of the simplest way to do it—and a quite fast way—is the old algorithm invented by a greek guy named Eratosthenes of Cyrene. OK, he was greek, so he wrote his name most probably Ἐρατοσθένης.

We are not really interrested in the literacy of ancient greeks but in their inventions. and Eratosthenes invented a lot One of those findings was a prime sieve and it got even named after him!
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Theorems I

Theorem of Quasi-Infinitenes Any number sufficiently large is indistinguishable from infinity by the imaginative power of the average human alone.

Corollary 1 Any sufficiently large part of an astonishing large number is still an astonishing large number.

Corollary 2 Any sufficiently small number subtracted from an astonishing large number results in a still astonishing large number.

On the numerical evaluation of factorials I

Introduction

This is the first post of what will be a very long series about calculating factorials and it is even a long way to the first calculation of a factorial.
At first let us build something for the actual calculations that is able to do it with arbitrary precision, do it fast enough and does not need any special software. A good compromise would be Javascript: it is build-in in every browser, rarely switched off if used locally, a lot of tutorials are
available for free and for money, and the author has a lot of that stuff already written. The last argument is the winning one, of course.
Oh, and: yes, this implementation will be with FFT!
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