# Reconstruction of Vega's Prime Number Table

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

In 1797 Vega published a table of prime numbers from 102001 to 400031. On each of the pages 88–127 there are 600 numbers in 10 columns with 60 numbers. Page 128 has 6 columns with 16 numbers. While there are no mistakes on this page, there are on some other pages. This reconstruction corrects some of the mistakes.

[more]
Contributed by: Izidor Hafner (August 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in 1797 or 1798 that is approximated by the function , where and are unspecified constants [1].

Carl Friedrich Gauss considered the same question as we see from a letter to Encke (1849), where Vega's tables were mentioned.

Vega's 1797 table of primes was based on Felkel's table [2].

References

[1] Wikipedia. "Prime Number Theorem." (Aug 18, 2013) en.wikipedia.org/wiki/Prime_number_theorem # Approximations_for _the _nth _prime _number.

[2] D. Roegel. "A Reconstruction of Vega's Table of Primes and Factors." (October 9, 2011) locomat.loria.fr/vega1797/vega1797doc.pdf.

[3] G. Vega, *Logarithmische, trigonometrische, und andere zum Gebrauche der Mathematik eingerichtete Tafeln und Formeln*, Leipzig: Weidmannischen Buchhandlung, 1797. www.dlib.si/details/URN:NBN:SI:DOC-OY967PMX/?browse=knjige&node=besedila%2f3&pageSize=25&query=%27source%3dknjige%40AND%40UDC%3dMatematika%40AND%40keywords%3dvega%27.

## Permanent Citation