Re-extending Chebyshev’s theorem about Bertrand’s conjecture
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...
Збережено в:
| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/172524 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Re-extending Chebyshev’s theorem about Bertrand’s conjecture / Armіn Shams // Український математичний журнал. — 2007. — Т. 59, № 12. — С. 1701–1706. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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