Prime divisors of shifted factorials

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
17 Downloads (Pure)


For any positive integer n we let P(n) be the largest prime factor of n. We improve and generalize several results of P. Erdos and C. Stewart on P(n!+1). In particular, we show that limsupn→∞P(n!+1)/n ≥ 2.5, which improves their lower bound of limsupn→∞P(n!+1)/n > 2.

Original languageEnglish
Pages (from-to)809-817
Number of pages9
JournalBulletin of the London Mathematical Society
Issue number6
Publication statusPublished - Dec 2005


Dive into the research topics of 'Prime divisors of shifted factorials'. Together they form a unique fingerprint.

Cite this