**Skewes’ Number:**

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.

**Numberphile Video:**

Hope you enjoyed this quick maths bite! M x

Advertisements

## One comment