# [seqfan] Re: Smallest emirp with emirp number of digits and emirp digital sum

Jonathan Post jvospost3 at gmail.com
Thu Nov 19 08:25:31 CET 2009

```I appreciate that!

"Emirps (A006567) with emirp number of digits and emirp digital sum"

{p: p in A006567 and A055642(p) in A006567 and A007953(p) in A006567}.

It seems to me that enough people responded to make this worth
submitting.  It would have 3 authors: myself, and the two gentlemen
who corrected/extended --  Ray Chandler <rayjchandler at sbcglobal.net>
(who found the first 4 elements, enough to submit), and zak seidov
<zakseidov at yahoo.com> who found more than the form will hold (but this
is not nice enough to deserve a b-list, I think).

Thank you both.  Ray, should you submit it thus, as associate editor
on the scene, and someone who has helped me so often over the years?

I'm not personally eager to look at 17-digit examples...

Best,

Jonathan Vos Post

On Wed, Nov 18, 2009 at 8:58 PM, zak seidov <zakseidov at yahoo.com> wrote:
> Here is the list
> of emirp and with emirp sum of digits (T)
> and emirp number of digits (=13 and not given)
> --- On Wed, 11/18/09, Jonathan Post <jvospost3 at gmail.com> wrote:
>
>> From: Jonathan Post <jvospost3 at gmail.com>
>> Subject: [seqfan] Smallest emirp with emirp number of digits and emirp digital sum
>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>> Date: Wednesday, November 18, 2009, 10:19 PM
>> Is 1000000004161 the smallest emirp
>> (A006567)  with emirp number of
>> digits and emirp digital sum?
>> It is prime, its reversal 1614000000001 is prime, it has a
>> prime  13
>> digits, R(13) = 31 is prime, and the
>> sum of digits 1+6+1+4+0+0+0+0+0+0+0+0+1 = 13 is prime (and
>> reversed is
>> again the prime 31).
>>
>> Or did I miss a smaller example in my sloppy by-hand
>> search?
>> {p,T}:
> {{1000000001159,17},{1000000002217,13},{1000000003463,17},{1000000004161,13},{1000000005713,17},{1000000005911,17},{1000000006037,17},{1000000006451,17},{1000000006699,31},{1000000007333,17},{1000000009403,17},{1000000010249,17},{1000000010447,17},{1000000010483,17},{1000000011019,13},{1000000011347,17},{1000000011383,17},{1000000013039,17},{1000000013503,13},{1000000014173,17},{1000000015127,17},{1000000015879,31},{1000000018489,31},{1000000019569,31},{1000000020307,13},{1000000020563,17},{1000000021333,13},{1000000022921,17},{1000000023713,17},{1000000024613,17},{1000000025009,17},{1000000026877,31},{1000000027111,13}}
> Hope it helps (& OK ;-)),
> Zak
>
>> For people who hate the word "emirp" this may be the worst
>> seq yet
>> encountered .. this an the 2nd smallest, 3rd smallest,
>> etc.
>>
>>
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```