Brief Communications

Ukrainian Mathematical Journal

, Volume 59, Issue 12, pp 1914-1921

First online:

Re-extending Chebyshev’s theorem about Bertrand’s conjecture

  • A. ShamsAffiliated withThe University of ManchesterFerdowsi University of Mashhad

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In this paper, Chebyshev’s theorem (1850) about Bertrand’s conjecture is re-extended using a theorem about Sierpinski’s conjecture (1958). The theorem had been extended before several times, but this extension is a major extension far beyond the previous ones. At the beginning of the proof, maximal gaps table is used to verify initial states. The extended theorem contains a constant r, which can be reduced if more initial states can be checked. Therefore, the theorem can be even more extended when maximal gaps table is extended. The main extension idea is not based on r, though.