Comment on A117078 : 2, 3, 7 : primes for which ln(A000040(n)) < SQRT(A001223(n))

[Jonathan Post]

Mathematics, abstract
math.NT/0611761

From: Bakir Farhi [view email
<http://arxiv.org/auth/show-email/09dd435c/math/0611761>]
Date: Fri, 24 Nov 2006 17:24:53 GMT   (8kb)

Formulas giving prime numbers under Cramér's conjecture Authors: * Bakir
Farhi <http://arxiv.org/find/math/1/au:+Farhi_B/0/1/0/all/0/1>*
Comments: 9 pages
Subj-class: Number Theory
MSC-class: 11A41

Under Cram\'er's conjecture concerning the prime numbers, we prove that for
any $x>1$, there exists a real $A=A(x)>1$ for which the formula $[A^{n^x}]$
(where $[]$ denotes the integer part) gives a prime number for any positive
integer $n$. Under the same conjecture, we also prove that for any
$\epsilon>0$, there exists a positive real number $B$ for which the formula
$[B.{n!}^{2+\epsilon}]$ gives a prime number for any sufficiently large
positive integer $n$.



On 12/10/06, reismann at free.fr <reismann at free.fr> wrote:
>
> Hi
>
> conjecture 2 = Cramér's conjecture.
> But I am surprised that :
> "Primes for which A117078(n) = 0" = "Primes for which ln(A000040(n)) <
> SQRT(A001223(n))"
>
> Rémi EISMANN
>
>
> Selon reismann at free.fr:
>
> > Dear Seqfans,
> >
> > I will submit this comment on January on A117078 :
> >
> > Subject: COMMENT FROM Remi Eismann RE A117078
> > %I A117078
> > %C A117078 Conjecture 1 : A117078(n) = 0 only for primes 2, 3 and 7.
> > Conjecture 2 : 2, 3, 7 : primes for which ln(A000040(n)) <
> SQRT(A001223(n)).
> > This sequence is finite and complete.
> > %O A117078 0
> > %K A117078 ,nonn,
> > %A A117078 Remi Eismann (reismann at free.fr), Dec 10 2006
> >
> > Any comments on the powerful conjecture 2 ?
> >
> > Rémi Eismann
> >
>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20061210/99ac40d6/attachment-0002.htm>