[seqfan] Re: Concatenate 5 digits = prime
Alexander Povolotsky
apovolot at gmail.com
Fri Mar 27 16:41:55 CET 2009
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
>> *immediate* contradiction
>>
>> 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.
More information about the SeqFan
mailing list