Corrected On sequence nXn where x equal 09,18,27,36,45,54,63,72,81,90

[Karima MOUSSAOUI]

Dear Farideh,
For example there are no prime on the form p07p 
(p between 999973 and 10000017 ).
99997307999953
100000170710000017
there are similar for 14,21, ...
thanks




> Message du 28/02/04 18:45
> De : f.firoozbakht at sci.ui.ac.ir
> A : bouyao 
> Copie à : Richard Guy , seqfan at ext.jussieu.fr
> Objet : Re: Corrected On sequence nXn where x equal 09,18,27,36,45,54,63,72,81,90
> 
> > for p11p
> > p=999931
> > for example p11p= 99993111999931 is prime
> > and the next is 100003031110000303
> 
> Dear bouyao,
> 
> For every natural number k there doesn't exist number
> n between 10^(2k-2) and 10^(2k-1) such that n.11.n is
> prime, because if number of digits of n is odd then n.11.n
> is divisible by 11.
> (Note that if ai is one digit number then 11 divides a1.a2.a3....as 
> Iff 11 divides a1-a2+a3-...+-as)
> So if prime p ( number m )is in following intervals;
> 
> [10^0,10^1], [10^2,10^3], [10^4,10^5], [10^6,10^7], [10^8,10^9],...
> 
> then p.11.p ( m.11.m ) is composite. 
> 
> But there is no similar statement for numbers 07,14,21 and 85 that 
> you wrote.(Instead of 11 we can write every multiple of 11 with even
> number of digits.)
> 
> Regards
> 
> Farideh
> 
> 
> 
> 
> ----------------------------------
> This mail sent through UI webmail.
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20040229/fc24a29d/attachment-0001.htm>