SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 10 - Sayı: 10

Notes on Sophie Germain Primes

Canan AKIN
Recep BAŞTAN
Pages
18–21
Publication Date
2022-11-05
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, in this paper, we give a characterization of Sophie Germain primes via a congruence.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a pair of Sophie Germain prime and connected safe prime is referred to as S G-S -primepair in short.
📊
Key Findings & Data:We formsome certain instructions for a sieve as an elementary method to find the S G-S -prime pairs and we also give anexample in which we use our instructions to obtain the S G-S -prime pairs up to 250.Wilson’s fundamental theorem in number theory gives a characterization of prime numbers via a congruence.
💡
Conclusion & Impact:Moreover, in this paper, we give a characterization of Sophie Germain primes via a congruence.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, a pair of Sophie Germain prime and connected safe prime is referred to as S G-S -primepair in short. We focus on a characterization to obtain S G-S -prime pairs owing to an eliminating method. We formsome certain instructions for a sieve as an elementary method to find the S G-S -prime pairs and we also give anexample in which we use our instructions to obtain the S G-S -prime pairs up to 250.Wilson’s fundamental theorem in number theory gives a characterization of prime numbers via a congruence. Moreover, in this paper, we give a characterization of Sophie Germain primes via a congruence.

🔖

Cite This Article

AKIN, C., BAŞTAN, R. (2022). Notes on Sophie Germain Primes. Turkish Journal of Mathematics and Computer Science, Cilt: 10 - Sayı: 10, 18–21. https://ajindex.com/articles/609172

📄 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.
  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.