Some thoughts on pseudoprimes
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We consider several problems about pseudoprimes. First, we look at the
issue of their distribution in residue classes. There is a literature on this topic in the case
that the residue class is coprime to the modulus. Here we provide some robust statistics in
both these cases and the general case. In particular we tabulate all even pseudoprimes to
1016. Second, we prove a recent conjecture of Ordowski: the set of integers n which are a
pseudoprime to some base which is a proper divisor of n has an asymptotic density.
Ključne reči:
pseudoprime / Carmichael numberIzvor:
Bulletin T.CLIV de l’Académie serbe des sciences et des arts, 2021, 53-72Izdavač:
- Beograd : Académie Serbe des sciences et des arts
Napomena:
- Bulletin t. 154 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 46
TY - CONF AU - Pomerance, Carl AU - Wagstaff, Samuel S. Jr. PY - 2021 UR - https://dais.sanu.ac.rs/123456789/13283 AB - We consider several problems about pseudoprimes. First, we look at the issue of their distribution in residue classes. There is a literature on this topic in the case that the residue class is coprime to the modulus. Here we provide some robust statistics in both these cases and the general case. In particular we tabulate all even pseudoprimes to 1016. Second, we prove a recent conjecture of Ordowski: the set of integers n which are a pseudoprime to some base which is a proper divisor of n has an asymptotic density. PB - Beograd : Académie Serbe des sciences et des arts C3 - Bulletin T.CLIV de l’Académie serbe des sciences et des arts T1 - Some thoughts on pseudoprimes SP - 53 EP - 72 UR - https://hdl.handle.net/21.15107/rcub_dais_13283 ER -
@conference{ author = "Pomerance, Carl and Wagstaff, Samuel S. Jr.", year = "2021", abstract = "We consider several problems about pseudoprimes. First, we look at the issue of their distribution in residue classes. There is a literature on this topic in the case that the residue class is coprime to the modulus. Here we provide some robust statistics in both these cases and the general case. In particular we tabulate all even pseudoprimes to 1016. Second, we prove a recent conjecture of Ordowski: the set of integers n which are a pseudoprime to some base which is a proper divisor of n has an asymptotic density.", publisher = "Beograd : Académie Serbe des sciences et des arts", journal = "Bulletin T.CLIV de l’Académie serbe des sciences et des arts", title = "Some thoughts on pseudoprimes", pages = "53-72", url = "https://hdl.handle.net/21.15107/rcub_dais_13283" }
Pomerance, C.,& Wagstaff, S. S. Jr.. (2021). Some thoughts on pseudoprimes. in Bulletin T.CLIV de l’Académie serbe des sciences et des arts Beograd : Académie Serbe des sciences et des arts., 53-72. https://hdl.handle.net/21.15107/rcub_dais_13283
Pomerance C, Wagstaff SSJ. Some thoughts on pseudoprimes. in Bulletin T.CLIV de l’Académie serbe des sciences et des arts. 2021;:53-72. https://hdl.handle.net/21.15107/rcub_dais_13283 .
Pomerance, Carl, Wagstaff, Samuel S. Jr., "Some thoughts on pseudoprimes" in Bulletin T.CLIV de l’Académie serbe des sciences et des arts (2021):53-72, https://hdl.handle.net/21.15107/rcub_dais_13283 .