In number theory
, de Polignac's formula
, named after Alphonse de Polignac
, gives the prime decomposition
of the factorial n
!, where n
≥ 1 is an integer
≥ 1 be an integer. Then the prime decomposition of n
! is given by
and the brackets represent the floor function.
Note that, for any real number x, and any integer n, we have:
which allows one to more easily compute the terms sp(n).