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

[f.firoozbakht at sci.ui.ac.ir]

> 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




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