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Diskr. Mat., 2008, Volume 20, Issue 2, Pages 15–24 (Mi dm1000)  

Testing numbers of the form $N=2kp_1^{m_1}p_2^{m_2}\cdots p_n^{m_n}-1$ for primality

E. V. Sadovnik


Abstract: We suggest an algorithm to test numbers of the form $N=2kp_1^{m_1}p_2^{m_2}\cdots p_n^{m_n}-1$ for primality, where $2k<p_1^{m_1}p_2^{m_2}\cdots p_n^{m_n}$, $k$ is an odd positive integer, $\pi$ is a prime number, $i=1,…,n$, and $p_1p_2\cdots p_n=3\pmod4$. The algorithm makes use of the Lucas functions. The algorithm suggested is of complexity $\widehat O(\log^2N)$.

DOI: https://doi.org/10.4213/dm1000

Full text: PDF file (128 kB)
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English version:
Discrete Mathematics and Applications, 2008, 18:3, 239–249

Bibliographic databases:

UDC: 511.2
Received: 21.06.2006
Revised: 30.01.2007

Citation: E. V. Sadovnik, “Testing numbers of the form $N=2kp_1^{m_1}p_2^{m_2}\cdots p_n^{m_n}-1$ for primality”, Diskr. Mat., 20:2 (2008), 15–24; Discrete Math. Appl., 18:3 (2008), 239–249

Citation in format AMSBIB
\Bibitem{Sad08}
\by E.~V.~Sadovnik
\paper Testing numbers of the form $N=2kp_1^{m_1}p_2^{m_2}\cdots p_n^{m_n}-1$ for primality
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 2
\pages 15--24
\mathnet{http://mi.mathnet.ru/dm1000}
\crossref{https://doi.org/10.4213/dm1000}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2450030}
\zmath{https://zbmath.org/?q=an:05618980}
\elib{http://elibrary.ru/item.asp?id=20730240}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 3
\pages 239--249
\crossref{https://doi.org/10.1515/DMA.2008.019}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-47249132989}


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  • Дискретная математика
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