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

[bouyao]

Dear Farideh,

Thank you very much for your help.

I remark that if p is prime , there are :
no prime numbers between 10^5 and 10^6 for p07p
no prime numbers betwen 10^6 and  10^7 for p14p
no prime numbers betwen 10^7 and 10^8 for p21p
...
no prime numbers betwen 10^5, 10^6 for p85p

there are anothers numbers that have this remark (p11p,...)

have you  information Why certain numbers have this remark ?

we can extended this numbers (pnpnpnp..p)

thanks.



----- Original Message ----- 
From: <f.firoozbakht at sci.ui.ac.ir>
To: "Karima MOUSSAOUI" <bouyao at wanadoo.fr>
Cc: "Richard Guy" <rkg at cpsc.ucalgary.ca>; <seqfan at ext.jussieu.fr>
Sent: Friday, February 27, 2004 11:35 PM
Subject: Re: Corrected On sequence nXn where x equal
09,18,27,36,45,54,63,72,81,90


>
> > Can anyone find n such that n09n,
> > n18n,n27n,n36n,n45n,n54n,n63n,n72n,n81n,n90n, are all primes
> >
> > where n09n designe concatenation of (n 09 n) (example 1091 is prime,
> > 310931 is prime)
>
>
> If we define a(m) as the smallest number n such that
> all the m numbers :
>
>           n.09.n, n.2*9.n, ...,n.(m-1)*9.n & n.m*9.n
>
> are primes, in fact you want a(10).
>
> The first six terms of this sequence are :
>
>                               1,47,251,9269,15533,1763897
>
> example: 1763897 is the smallest number n such that all six numbers
> n.09.n, n.18.n, ...,n.54.n are primes.
> (1763897091763897,1763897181763897,1763897271763897,1763897361763897,
> 1763897451763897 & 1763897541763897  are primes.)
>
> I think we can find at most two more terms of this sequence and a(10)
> is too large ,so we can not find it.
>
> Regards
>
> Farideh
>
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