Rosser's theorem, published by J. Barkley Rosser in 1939 in the Proceedings of the London Mathematical Society, gives a lower bound on the growth of the primes: it states that the nth prime number exceeds n times the natural logarithm of n, for every n of at least 1. Pierre Dusart later sharpened the bound in 1999, showing that the nth prime exceeds n times the sum of the natural logarithm of n, the natural logarithm of the natural logarithm of n, and negative one, for n of at least 2, illustrating how later work refined Rosser's original estimate. 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
Partially Attested
Proof YearSource gives the publication year, not an explicit proof year. Classification
Statement Form StatementThe nth prime p_n is greater than n log n, for n at least 1. 2 Connections
Has Statement Form
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.
In Branch
Source Rosser's theorem (Wikipedia)
Sources
1. Wikipedia: Rosser's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
>n\log n.} In 1999, Pierre Dusart proved a tighter lower bound for n ≥ 2 : p n > n ( log n + log log n − 1 ) .
2. Rosser's theorem (Wikipedia)
Introduction, full statement
p_n>n\log n
Introduction, sentence 2
It was published by J. Barkley Rosser in 1939.
- In Branch: Number Theory, Lead sentence
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