where π(x) is the prime-counting function and li(x) is logarithmic integral function.

Prime Counting Function: is the function counting the number of prime numbers less than or equal to some real number x.

Logarithmic Integral Function: used in prime number theorem as an estimate of the number of prime numbers less than a given value.

In 1912, it was proved by Littlewood that this limit existed, and it – Skewes’ number – was subsequently found by Stanley Skewes, South African mathematician, in 1933.

However this limit has been improved to by Lehman in 1966.

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