Prime Numbers

Paper Summary:

This paper explains that prime numbers have upset humanity for the last 2,300 years, ever since Euclid proved that there was infinity. The paper presents Euclid's proof. The author points out that, in the 19th century, the Russian, Tchebychef ,made significant contributions to the study of prime numbers by concluding that if the B(x) from Legendre's equation had a limit, then that limit had to be 1. The paper relates that Bernhardt Riemann, in 1859, continued Euler's work on series of numbers and made fundamental new discoveries within the prime numbers domain.

From the Paper:

"Let x be a positive real number and let us define " (x) as the number of primes less or than equal to x. " (x) is a function and will be studied as such. For small values of x, we can intuit the values for " (x). Thus, for example, if x is 10, then the primes less then 10 are 2, 3, 5 and 7, so that " (10) is 4. Similarly, " (24) = 9. Our concern is for very large values of x."

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