Skewes’ number is the number above which
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.
Hope you enjoyed this quick maths bite! M x