Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme
Theorem

Hardy-Ramanujan Theorem

Number Theory

The Hardy-Ramanujan theorem is a result in number theory, proved by Srinivasa Ramanujan and checked by G. H. Hardy, stating that the normal order of the number of distinct prime factors of a number n is the logarithm of the logarithm of n. Roughly speaking, this means that most numbers have approximately this many distinct prime factors. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Identity or Equation 1
Statement
The normal order of the number of distinct prime factors of n is log log n. 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Proved By

Source Hardy-Ramanujan theorem (Wikipedia)
Sources
1. Hardy-Ramanujan theorem (Wikipedia)
  • Introduction, first sentence
    the normal order of the number
  • Proved By: Srinivasa Ramanujan, Lead paragraph
    proved by Ramanujan and checked by Hardy
View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.