In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer
They are named after Carl Størmer.
The first few Størmer numbers are: John Todd proved that this sequence is neither finite nor cofinite.
[1] More precisely, the natural density of the Størmer numbers lies between 0.5324 and 0.905.
It has been conjectured that their natural density is the natural logarithm of 2, approximately 0.693, but this remains unproven.
[2] Because the Størmer numbers have positive density, the Størmer numbers form a large set.
as sums of Gregory numbers for integers (arctangents of unit fractions).
may be decomposed by repeatedly multiplying the Gaussian integer
, in order to cancel prime factors
is chosen to be a Størmer number such that