SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Volume: 10 Special Issue

Notes on Sophie Germain Primes

Recep Baştan(GİRESUN ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)
Canan Akın(GİRESUN ÜNİVERSİTESİ)0000-0002-8922-3272
Pages
—
Publication Date
2018-12-29
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover we give an example in which we use our instructions to obtain the SG-S-prime pairs up to $250$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An elementary method for eliminating $2m$-prime pairs is given by Lampret [S.
📊
Key Findings & Data:Lampret, Sieving $2m$-prime pairs, Notes on Number Theory and Discrete Mathematics Vol. 20, 2014, No.3, 54-46.], where m is an arbitrary positive integer. 2m-prime pairs are related the twin prime pairs since a $2m$-prime pair is a twin prime pair if $m=1$.
💡
Conclusion & Impact:Moreover we give an example in which we use our instructions to obtain the SG-S-prime pairs up to $250$.
🔬Design:Conference Paper
📍Scope:2014 Verileri
⚙️Variables:Prime number · Sophie Germain primes · Safe Primes

Abstract

An elementary method for eliminating $2m$-prime pairs is given by Lampret [S. Lampret, Sieving $2m$-prime pairs, Notes on Number Theory and Discrete Mathematics Vol. 20, 2014, No.3, 54-46.], where m is an arbitrary positive integer. 2m-prime pairs are related the twin prime pairs since a $2m$-prime pair is a twin prime pair if $m=1$. Lampret gave a characterization for 6n-prime pairs of the form $(6k - 1, 6k + 6n - 1)$. In section 2, the Sophie Germain prime and connected safe prime pairs are referred to as $SG$-$S$-prime pairs in short. By using Lampret's results, we focus on a characterization to obtain SG-S-prime pairs owing to an eliminating method. Thus it is formed instructions for a sieve as an elementary method to find the $SG$-$S$-prime pairs. Moreover we give an example in which we use our instructions to obtain the SG-S-prime pairs up to $250$.

🔖

Cite This Article

Baştan, R., Akın, C. (2018). Notes on Sophie Germain Primes. Turkish Journal of Mathematics and Computer Science, Volume: 10 Special Issue. https://ajindex.com/articles/1324895

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (12)

  1. Alkalay-Houlihan C., Sophie Germain and Special Cases of Fermat’s Last Theorem. http://www.math.mcgill.ca/darmon/courses/12- 13/nt/projects/Colleen-Alkalay-Houlihan.pdf. Accessed: 2017-03-20.
  2. Bishop, S. A., Okagbue, H. I., Adamu, M. O., Olajide, F. A., Sequences of numbers obtained by digit and iterative digit sums of Sophie Germain primes and its variants, Global Journal of Pure and Applied Mathematics, 12(2)(2016), 1473-1480.
  3. Bucciarelli, L.L., Dworsky N., Sophie Germain: An essay in the history of the theory of elasticity, Vol. 6., Springer Science and Business Media, Netherland, 2012.
  4. Caldwell, C.K., Prime Pages. The Top Twenty: Sophie Germain. http://primes.utm.edu/top20/page.php?id=2.
  5. Clement, P. A., Congruences to sets of primes, Am. Math. Mon. 56 (1949), 23-25.
  6. Daniloff, L.L., The Work of Sophie Germain and Niels Henrik Abel on Fermat’s Last Theorem. MS thesis. 2017.
  7. Lampret, S., Sieving 2m-prime pairs, Notes on Number Theory and Discrete Mathematics 20 (2014), 54-46.
  8. Liu, F., On the Sophie Germain prime conjecture, WSEAS Transactions in Math 10, 2 (2011), 421-430.
  9. Meireles, M., On Sophie Germain primes. Proc. 13th WSEAS Int. Conf. App. Math. (2008), 370-373.
  10. Ribenboim, P., 13 Lectures on Fermat’s Last Theorem, Springer-Verlag, New York, 1979.
  11. Ribenboim, P., Fermat’s Last Theorem for Amateurs, Springer-Verlag, New York, 1999.
  12. Ribenboim, P., The Little Book of Bigger Primes, 2nd ed., Springer-Verlag, New York, 2004.