Questo numero è primo? Sì, forse, dipende ...

Luisella Caire; Umberto Cerruti

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-A, Issue: 3-1, page 449-481
  • ISSN: 0392-4041

Abstract

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In questo articolo presentiamo una breve panoramica di alcuni algoritmi il cui compito è decidere se un intero è primo: criteri di primalità, che sono deterministici (cioè rispondono con certezza sì e no) e incondizionati, ma purtroppo inefficienti (tecnicamente non polinomiali); algoritmi efficienti, ma solo probabilistici (cioè che danno la certezza quando rispondono no mentre nel caso di risposta sì assicurano soltanto un limite inferiore alla probabilità che il numero sia primoo; algoritmi che sono al tempo stesso deterministici ed efficienti, ma sono condizionati, cioè dipendono dalla congettura estesa di Rienman, tuttora non dimostrata.

How to cite

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Caire, Luisella, and Cerruti, Umberto. " Questo numero è primo? Sì, forse, dipende ...." Bollettino dell'Unione Matematica Italiana 9-A.3-1 (2006): 449-481. <http://eudml.org/doc/289587>.

@article{Caire2006,
abstract = {In this paper we outline some algorithms answering the question if a given number is prime: primally criteria, that are deterministic (they positively reply yes or not) and unconditional, but inefficient (technically not polynomial-time); algoritms that are efficient, but only probabilistic (to say they give absolute certainty if they answer not, whereas they only give a low boundary of the probability for the number to be prime if they answer yes); algorithms that are the same time deterministic and efficient, but conditioned, that is they depend on the extended Riemann conjecture(yet to be proved).},
author = {Caire, Luisella, Cerruti, Umberto},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {12},
number = {3-1},
pages = {449-481},
publisher = {Unione Matematica Italiana},
title = { Questo numero è primo? Sì, forse, dipende ...},
url = {http://eudml.org/doc/289587},
volume = {9-A},
year = {2006},
}

TY - JOUR
AU - Caire, Luisella
AU - Cerruti, Umberto
TI - Questo numero è primo? Sì, forse, dipende ...
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/12//
PB - Unione Matematica Italiana
VL - 9-A
IS - 3-1
SP - 449
EP - 481
AB - In this paper we outline some algorithms answering the question if a given number is prime: primally criteria, that are deterministic (they positively reply yes or not) and unconditional, but inefficient (technically not polynomial-time); algoritms that are efficient, but only probabilistic (to say they give absolute certainty if they answer not, whereas they only give a low boundary of the probability for the number to be prime if they answer yes); algorithms that are the same time deterministic and efficient, but conditioned, that is they depend on the extended Riemann conjecture(yet to be proved).
LA - ita
UR - http://eudml.org/doc/289587
ER -

References

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