Geodesic
New probabilistic primality test
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 2, Tome 479 (2019), pp. 121-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we present a new general probabilistic test for primality. The estimated efficiency of our test turns out to be inferior to that of the Miller–Rabin test. However, we provide some heuristic arguments that our estimation of efficiency is quite rough. This allows us to expect that the real efficiency of our test is much greater. 
@article{ZNSL_2019_479_a4,
     author = {A. G. Moshonkin and I. M. Khamitov},
     title = {New probabilistic primality test},
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     pages = {121--130},
     year = {2019},
     volume = {479},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_479_a4/}
}
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A. G. Moshonkin; I. M. Khamitov. New probabilistic primality test. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 2, Tome 479 (2019), pp. 121-130. http://geodesic.mathdoc.fr/item/ZNSL_2019_479_a4/

[1] R. M. Robinson, “Mersenne and Fermat Numbers”, Proc. Amer. Math. Soc., 5 (1954), 842–846 | DOI | MR | Zbl

[2] M. Agrawal, N. Kayal, N. Saxena, “Primes is in $P$”, Ann. of Math. (2), 160:2 (2004), 781–793 | DOI | MR | Zbl

[3] E. Lucas, “Theorie des fonctions numeriques simplement periodiques”, Amer. J. Math., 1:2–4 (1878), 184–240 (French) ; 289–321 | DOI | MR | Zbl

[4] W. R. Alford, A. Granville, C. Pomerance, “There are infinitely many Carmichael numbers”, Ann. of Math., 139 (1994), 703–722 | DOI | MR | Zbl

[5] R. Solovay, V. Strassen, “A fast Monte-Carlo test for primality”, SIAM J. Comput., 6:1 (1977), 84–85 | DOI | MR | Zbl

[6] M. O. Rabin, “Probabilistic algorithm for testing primality”, J. Number Theory, 12:1 (1980), 128–138 | DOI | MR | Zbl

[7] M. Baker, Cipolla's algorithm for finding square roots mod p, http://people.math.gatech.edu/m̃baker/pdf/cipolla2011.pdf