Reference : A conjecture on primes in arithmetic progressions and geometric intervals
E-prints/Working papers : First made available on ORBilu
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/45084
A conjecture on primes in arithmetic progressions and geometric intervals
English
Barthel, Jim Jean-Pierre mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS) >]
Müller, Volker mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS) >]
Undated
No
[en] Primes in Arithmetic Progressions ; Linnik's constant ; Carmichael's conjecture
[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.
http://hdl.handle.net/10993/45084

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