# Erdős arcsine law

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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 *j*th 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

## References

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