Reconstruction of Vega's Prime Number Table
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]
We take the last numbers on each page of Vega's table (all are prime) and count the exact number of primes between the two consecutive last numbers. If Vega's table was correct, these numbers would be all 600. If the number is 599, than an incorrect number is included. If the number is 601, a prime is missing.
On page 92, the prime number 135727 is recorded twice. In these ways we see that there are four prime numbers missing from Vega's table.
We did not consider the possibility that on a page there is a prime missing and a composite number included.[less]
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 .
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 .
 Wikipedia. "Prime Number Theorem." (Aug 18, 2013) en.wikipedia.org/wiki/Prime_number_theorem # Approximations_for _the _nth _prime _number.
 D. Roegel. "A Reconstruction of Vega's Table of Primes and Factors." (October 9, 2011) locomat.loria.fr/vega1797/vega1797doc.pdf.
 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.