On the divergence of series of reciprocals of the Baťa prime numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00619402" target="_blank" >RIV/67985840:_____/24:00619402 - isvavai.cz</a>
Result on the web
<a href="http://home.pf.jcu.cz/~sbml/wp-content/uploads/2024_Krizek.pdf" target="_blank" >http://home.pf.jcu.cz/~sbml/wp-content/uploads/2024_Krizek.pdf</a>
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
On the divergence of series of reciprocals of the Baťa prime numbers
Original language description
In this note, we introduce a new class of prime numbers - Baťa primes. A positive integer is called a Baťa prime of class k, if it ends with at least k 9s. We prove that for any positive integer k there exist infinitely many Baťa primes of class k. Some generalizations of this statement to other end digits are given as well. By means of the Stieltjes integral and the Prime Number Theorem for arithmetic progressions we also prove that the sum of reciprocal values of the Baťa primes is infinity.
Czech name
—
Czech description
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)