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On the proximity of large primes

In: Mathematica Slovaca, vol. 68, no. 5
Minjia Shi - Florian Luca - Patrick Solé
Detaily:
Rok, strany: 2018, 981 - 986
Kľúčové slová:
primes, numeration basis, coding theory
O článku:
By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis $q$, we show that there are infinitely many pairs of primes the base $q$ expansion of which differ in at most two digits. Likewise, for any fixed integer $t$, there are infinitely many pairs of primes, the first $t$ digits of which are the same. In another direction, we show that, there is a constant $c$ depending on $q$ such that for infinitely many integers $m$ there are at least $c log log m$ primes which differ from $m$ by at most one base $q$ digit.
Ako citovať:
ISO 690:
Shi, M., Luca, F., Solé, P. 2018. On the proximity of large primes. In Mathematica Slovaca, vol. 68, no.5, pp. 981-986. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0160

APA:
Shi, M., Luca, F., Solé, P. (2018). On the proximity of large primes. Mathematica Slovaca, 68(5), 981-986. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0160
O vydaní:
Publikované: 31. 10. 2018