Eprint first made available on ORBilu (E-prints, Working papers and Research blog)
A conjecture on primes in arithmetic progressions and geometric intervals
Barthel, Jim Jean-Pierre; Müller, Volker
n.d.
 

Files


Full Text
PrimesInAP.pdf
Author preprint (343.1 kB)
Request a copy
Annexes
(4) Commented Code.txt
(6.08 kB)
Request a copy

All documents in ORBilu are protected by a user license.

Send to



Details



Keywords :
Primes in Arithmetic Progressions; Linnik's constant; Carmichael's conjecture
Abstract :
[en] We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive integers, contains at least one prime from each coprime congruence class. We prove this conjecture first unconditionally for all 2≤q≤45000 and all t≥1 and second under ERH for almost all q≥2 and all t≥2. Furthermore, we outline heuristic arguments for the validity of the conjecture beyond the proven bounds and we compare it with related long-standing conjectures. Finally, we discuss some of its consequences.
Disciplines :
Mathematics
Author, co-author :
Barthel, Jim Jean-Pierre ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Müller, Volker ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Language :
English
Title :
A conjecture on primes in arithmetic progressions and geometric intervals
Publication date :
n.d.
Available on ORBilu :
since 15 December 2020

Statistics


Number of views
85 (12 by Unilu)
Number of downloads
5 (4 by Unilu)

Bibliography


Similar publications



Contact ORBilu