Legendre's constant

The Legendre 's constant is a mathematical constant that occurs in a 1798 prepared by Adrien -Marie Legendre formula to estimate the number of primes that are not n is greater than a given number. Their value was later shown to be exactly 1.

Legendre suspected due to his considering the frequency of prime numbers that the following limit exists:

Wherein the natural logarithm of n, the number of prime numbers that are not greater than N, and B is the Legendre constant that Legendre by means of calculations to first n = 400 000, and later n = one million to about 1.08366 estimated. From the existence of the constants follows, regardless of their exact value, the prime number theorem.

Later, Carl Friedrich Gauss investigated further the allegedly existing constant and assumed that their value might be lower. Charles -Jean de La Vallée Poussin and Jacques Hadamard independently proved the prime number theorem in 1896, and de la Vallée Poussin showed that B = 1.