# [seqfan] Re: Concatenate 5 digits = prime

Eric Angelini Eric.Angelini at kntv.be
Fri Mar 27 17:04:37 CET 2009

```Hello Alexander and SeqFans,

A few results here (mostly french language) :

Concatenation seems to work infinitely (no proof yet) for
2, 3 and 4 digits -- not more.
Best,
É.

-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] De la part de Alexander Povolotsky
Envoyé : vendredi 27 mars 2009 16:42
À : Sequence Fanatics Discussion list; jeanmarcfalcoz at vtxnet.ch
Objet : [seqfan] Re: Concatenate 5 digits = prime

As it is easily observable from terms so far available (sorry for
stating the obvious)
- not counting single occurence of 2, the digits involved are seems
to be only: 1, 3, 9 and ocasionally 7 ...

If this sequence is by any chance happens to be infinite (as it was
already asked by Eric), would this digit pattern remain and if so,
would it be interesting to evaluate the frequencies of each of those
digits more precisely ?

Regards,
ARP
==============================================
On Fri, Mar 27, 2009 at 7:52 AM, Jean-Marc Falcoz
<jeanmarcfalcoz at vtxnet.ch> wrote:
> Hello !
>
> I believe it's the sequence for the concatenation of 4 digits, not 5
>
> 1237, 2371, 3719, etc are prime numbers.
>
> For 5 digits, the sequence is finite : {1, 2, 3, 4, 7, 39}  because there is
> no 5 digit prime beginning with 4739
>
> On Thu, Mar 26, 2009 at 11:52 AM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
>>
>> Hello SeqFans,
>>
>> Jean-Marc Falcoz has computed this seq. :
>>
>> 1,2,3,7,19,31,91,373,931,1931,1933,7193,11931,19311,93119,311931,
>> 913733,1373313,7331373,9311931,19311931,19311933,71931193,119311931,
>> 193119311,931193119,3119311931,9137331373,9311931193,...
>>
>> ... where any concatenation of 5 consecutive digits is a prime.
>>
>> We clearly have a(1) = 1
>> and a(n) smallest integer > a(n-1) not leading to an
>>
>> Is the seq infinite?
>>
>> ---
>>
>> The seq where any concatenation of 6 consecutive digits is a prime
>> stops immediately:
>>
>> 1,2,3,4,5,7
>> the only possibility being 1,2,3,4,5,7,1 -- but no 6-digit prime
>> starts with 34571-
>>
>> ... stops immediately unless we drop the above *immediate* constraint
>> (but the resulting seq might be too heavy to compute with brute force
>> (trials and errors).
>>
>> Best,
>> É.

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