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On the proximity of large primes.
- Source :
- Mathematica Slovaca; Oct2018, Vol. 68 Issue 5, p981-986, 6p
- Publication Year :
- 2018
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- INTEGERS
CODING theory
NUMBER systems
PRIME numbers
COMBINATORICS
Subjects
Details
- Language :
- English
- ISSN :
- 01399918
- Volume :
- 68
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Mathematica Slovaca
- Publication Type :
- Academic Journal
- Accession number :
- 132691893
- Full Text :
- https://doi.org/10.1515/ms-2017-0160