Document Zbl 1469.11374

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Primitive and geometric-progression-free sets without large gaps. (English) Zbl 1469.11374

Acta Arith. 192, No. 1, 95-104 (2020).

Summary: 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 X. He [J. Number Theory 151, 197–210 (2015; Zbl 1325.11014)] for gaps in -free sets.

Cited in 2 Documents

MSC:

11N25	Distribution of integers with specified multiplicative constraints
11B05	Density, gaps, topology

Keywords:

geometric-progression-free sets; gaps

Citations:

Zbl 1325.11014

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