# [seqfan] Re: Sum of digits of primes - not divisible by 3?

Neil Sloane njasloane at gmail.com
Sat Nov 3 03:20:35 CET 2018

```Georg,  A number > 3 whose digit sum is a multiple of 3 is always divisible
by 3, so cannot be prime.

But the other direction is an unsolved problem.  We don't know that if  we
are given k>3 and not a multiple of 3 then there is a prime with digit sum k

I did some editing to make the point clearer.

On Fri, Nov 2, 2018 at 8:20 PM Georg.Fischer <georg.fischer at t-online.de>
wrote:

> Dear Sequence Fans,
>
> in my "coincidences" scans I just stumbled over the
> following pair:
>
> A001651 Numbers not divisible by 3.
>          %K nonn,easy %O 1,2 %A N. J. A. Sloane
>
> A133223 A007605 [Sum of digits of n-th prime],
>          sorted and duplicates removed. ...
>          %K nonn,base %O 1,1 %A Lekraj Beedassy, Dec 19 2007
>          %C Presumably this is 3 together with numbers
>             greater than 1 and not divisible by 3.
>             - Charles R Greathouse IV, Jul 17 2013
>
> This is rather astonishing to me. Has it been proven
> in the meantime? Is it contained in the paper of
> Mauduit and Rivat?
>
> Best regards - Georg
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```