Some explicit results on the sum of a prime and an almost prime
Abstract
Inspired by a classical result of Rényi, we prove that every even integer $N\geq 4$ can be written as the sum of a prime and a number with at most 369 prime factors. We also show, under assumption of the generalised Riemann hypothesis, that this result can be improved to 33 prime factors.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.01229
- arXiv:
- arXiv:2208.01229
- Bibcode:
- 2022arXiv220801229J
- Keywords:
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- Mathematics - Number Theory;
- 11P32;
- 11N36 (Primary) 11N13 (Secondary)
- E-Print:
- 20 pages