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<p>Inspired by a classical result of Rényi, we prove that every even integer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N\geq 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> can be written as the sum of a prime and a number with at most 395 prime factors. We also show, under assumption of the generalised Riemann hypothesis, that this result can be improved to 31 prime factors. </p>

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Some explicit results on the sum of a prime and an almost prime

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • D. R. Johnston,
  • V. V. Starichkova

摘要

Inspired by a classical result of Rényi, we prove that every even integer \(N\geq 4\) N ≥ 4 can be written as the sum of a prime and a number with at most 395 prime factors. We also show, under assumption of the generalised Riemann hypothesis, that this result can be improved to 31 prime factors.