Identificación de candidatos a primos Mersenne mediante clasificación ova-angular utilizando aprendizaje automático con regresión SVM y Kernel Gaussiano

Yeisson Alexis Acevedo-Agudelo; Gabriel Ignacio Loaiza-Ossa

doi:10.33571/rpolitec.v19n37a7

Authors

Yeisson Alexis Acevedo-Agudelo Universidad EAFIT https://orcid.org/0000-0002-1640-9084
Gabriel Ignacio Loaiza-Ossa Universidad EAFIT https://orcid.org/0000-0003-2413-1139

DOI:

https://doi.org/10.33571/rpolitec.v19n37a7

Keywords:

Ova-angular rotations, Mersenne’s primes, Support Vector Machine, Gaussian Kernel.

Abstract

In this paper three prime numbers are presented as high potentials to be Mersenne numbers and their application in computational primality testing is suggested. These numbers are constructed from a regression algorithm based on Support vector machines (SVM) and using a Gaussian Kernel. Data training is carried out using the Phyton programming language, In the study we address the current data of Mersenne primes and work with the Ova-angular classification group for Mersenne primes .

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Author Biographies

Yeisson Alexis Acevedo-Agudelo, Universidad EAFIT

Magister en Matemáticas Aplicadas

Gabriel Ignacio Loaiza-Ossa, Universidad EAFIT

Doctor en Ciencias Matemáticas

References

Schölkopf, B., & Smola, A. (2002). Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT press.

Duda, R. O., Hart, P. E., & Stork, D. G. (2012). Pattern classification (2nd ed.). Wiley.

Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT press.

Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer Science & Business Media.

Burges, C. J. C. (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2), 121–167. https://doi.org/10.1023/A:1009715923555

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). Springer Science & Business Media.

Shawe-Taylor, J., & Cristianini, N. (2004). Kernel Methods for Pattern Analysis. Cambridge University Press.

Ghosh, S., Ghosh, A., & Ganguly, N. (2019). Using Support Vector Machines for Predicting Prime Numbers. Proceedings of the 2019 IEEE 6th Uttar Pradesh Section International Conference on Electrical, Electronics and Computer Engineering (UPCON). https://doi.org/10.1109/UPCON47194.2019.8975418

Granville, A. (2012). Prime numbers and cryptography. Notices of the American Mathematical Society, 59(10), 1430-1435.

Acevedo Y. (2021). Prime numbers: an alternative study using ova-angular rotations, JP Journal of Algebra, Number Theory and Applications 52(1), 127-161. DOI: 10.17654/NT052010127.

Acevedo Y. (2020). “A complete classification of the Mersenne’s primes and its implications for computing”, Revista Politécnica, vol.16, no.32pp.111-119. DOI:10.33571/rpolitec.v16n32a10.

Rivest, R. L. (1996). The MD5 Message-Digest Algorithm. RFC 1321. Internet Engineering Task Force.