Journal of Integer Sequences, Vol. 15 (2012), Article 12.5.4

Ramanujan and Labos Primes, Their Generalizations, and Classifications of Primes

Vladimir Shevelev
Department of Mathematics
Ben-Gurion University of the Negev
Beer-Sheva 84105


We study the parallel properties of the Ramanujan primes and a symmetric counterpart, the Labos primes. Further, we study all primes with these properties (generalized Ramanujan and Labos primes) and construct two kinds of sieves for them. Finally, we give a further natural generalization of these constructions and pose some conjectures and open problems.

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(Concerned with sequences A006992 A055496 A060715 A080359 A104272 A164288 A164294 A164333 A164368 A164554 A164952 A166251 A166252 A166307 A182365 A182366 A182391 A182392 A182423 A182426 A182451 A193507 A193761 A193880 A194184 A194186 A194217 A194598.)

Received August 4 2011; revised versions received September 7 2011; May 8 2012; May 16 2012. Published in Journal of Integer Sequences, May 29 2012.

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