# [seqfan] Re: Primes that are concatenation of the first n primes

zak seidov zakseidov at yahoo.com
Fri Dec 11 09:16:53 CET 2009

```Douglas,

1. you are right!
I should say "lexicographically least"!

and look for lexicographically least permutation
of n primes which gives a prime.

2. But your version is also correct and ... is
A083427 Smallest prime which is a concatenation of n distinct primes.
2, 23, 257, 2357, 112573, 11132357, 11131719257, 111317193257
2a. So you may send "more terms" to A083427!

3. Also notice that A053095 differs from A171437 (A053095(n)>=A171437(n)):

A053095  Number of primes having exactly same digits as appear in first n primes.
1, 1, 1, 8, 62, 568
3a. So you may wish to find "more terms" to A053095!

Thanks,
Zak
P.S.
4. I'll cc this to the list!

--- On Thu, 12/10/09, Douglas McNeil <mcneil at hku.hk> wrote:

> From: Douglas McNeil <mcneil at hku.hk>
> Subject: Re: [seqfan] Primes that are concatenation of the first n primes
> To: zakseidov at yahoo.com
> Date: Thursday, December 10, 2009, 10:54 PM
> Clarification:
>
> On the candidate sequence A171436, I'm a little confused.
>
> It begins
> 2,23,523,2357,235117,23571311,2351311177,235713111719,23571113191723.
>
> But isn't 112573 a concat-permutation of the first five
> primes (2 3 5
> 7 11) which is prime, and smaller
> than 235117?  In fact, I'd typically expect the
>
> I find:
>
> 2
> 23
> 523
> 2357
> 112573
> 11132357
> 1113257317
> 111317193257
> 11131719223357
>
> However, I seem to agree with the first 9 terms of
> A171437.   (I also
> seem to agree with A171438.)
>
> Am I missing something?  (I did this pretty quickly,
> so that's
> entirely possible.)
>
> Doug
>
> --
> Department of Earth Sciences
> University of Hong Kong
>

```