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Primitive and geometric-progression-free sets without large gaps

Volume 192 / 2020

Nathan McNew Acta Arithmetica 192 (2020), 95-104 MSC: Primary 11N25; Secondary 11B05. DOI: 10.4064/aa180921-4-2 Published online: 26 September 2019


We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of prime numbers. The proof uses the probabilistic method. Using the same techniques we improve the bounds obtained by He for gaps in geometric-progression-free sets.


  • Nathan McNewDepartment of Mathematics
    Towson University
    8000 York Road
    Towson, MD 21252, U.S.A.

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