Chebyshev's formula

A major unknown remains the distribution of prime numbers in different parts of the sequence of natural numbers. This distribution is shown in the following table:

 

There is no exact formula that would determine how many prime numbers are in different parts of the natural numbers, although many mathematicians have tried to create such a formula. The one who succeeded best was the Russian mathematician P.L. CHEBYSHEV (1821–1894), who created a formula by which he determined, with fairly high accuracy, the number of prime numbers between 1 and any natural number x.

 

 where π(x) is Chebyshev’s function.

 

Find out how many prime numbers (according to Chebyshev) are between 1 and 10⁷

 

Between 1 and 10⁷ there are about 688,666 prime numbers. Exactly, there are 664,579 prime numbers.

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