ERROR ESTIMATES FOR A CLASS OF CONTINUOUS BONSE-TYPE INEQUALITIES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019268" target="_blank" >RIV/62690094:18470/22:50019268 - isvavai.cz</a>
Result on the web
<a href="https://www.ams.org/journals/mcom/2022-91-337/S0025-5718-2022-03741-8/" target="_blank" >https://www.ams.org/journals/mcom/2022-91-337/S0025-5718-2022-03741-8/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/mcom/3741" target="_blank" >10.1090/mcom/3741</a>
Alternative languages
Result language
angličtina
Original language name
ERROR ESTIMATES FOR A CLASS OF CONTINUOUS BONSE-TYPE INEQUALITIES
Original language description
Let p(n) be the nth prime number. In 2000, Papaitopol proved that the inequality p(1)... p(n) > p(n+1)(n-pi(n)) holds, for all n >= 2, where pi(x) is the prime counting function. In 2021, Yang and Liao tried to sharpen this inequality by replacing n - pi(n) by n - pi(n) + pi(n)/pi(logn) - 2 pi(pi(n)), however there is a small mistake in their argument. In this paper, we exploit properties of the logarithm error term in inequalities of the type p(1) ... p(n) > p(n+1)(k(n, x)), where k(n, x) = n - pi(n) +pi(n)/pi(logn) - x pi(pi(n)). In particular, we improve Yang and Liao estimate, by showing that the previous inequality at x = 1.4 holds for all n >= 21.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics of Computation
ISSN
0025-5718
e-ISSN
1088-6842
Volume of the periodical
91
Issue of the periodical within the volume
337
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
2335-2345
UT code for WoS article
000802279400001
EID of the result in the Scopus database
2-s2.0-85134403942