Squarefree smooth numbers and Euclidean prime generators

Andrew R. Booker, Carl Pomerance

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
307 Downloads (Pure)


We show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.
Original languageEnglish
Pages (from-to)5035-5042
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number12
Early online date31 Aug 2017
Publication statusPublished - 1 Dec 2017


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