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 [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) >] | |

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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