Distribution of primes
- Category
- RIEMANN HYPOTHESIS
- Definition
- The study of how prime numbers are spaced and how their counting functions fluctuate around average trends.
- Math Level
- GENERAL
The distribution of primes means the way prime numbers are spaced among the positive integers.
Primes become less frequent on average as numbers grow, but their local spacing is irregular. The Prime Number Theorem captures the broad trend, while the zeros of the zeta function encode finer fluctuations; RH would sharply constrain those fluctuations.
See also: prime number, Prime Number Theorem, Riemann zeta function, Riemann Hypothesis..