Rahul Sharma (Editor)

Erdős arcsine law

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

In number theory, the Erdős arcsine law, named after Paul Erdős, states that the prime divisors of a number have a distribution related to the arcsine distribution.

Specifically, say that the jth prime factor p of a given number n (in the sorted sequence of distinct prime factors) is "small" when log log p < j. Then, for any fixed parameter u, in the limit as x goes to infinity, the proportion of the integers n less than x that have fewer than u log log n small prime factors converges to

2 π arcsin u .

References

Erdős arcsine law Wikipedia