# n^n is interprime, 2,6,9, n ~> 20,000

ZAKIRS zfseidov at ycariel.yosh.ac.il
Tue Sep 17 16:33:59 CEST 2002

```i'm not sure, but next n is as large as in subject. good luck to all. zak

-----Original Message-----
From: Neil Fernandez [mailto:primeness at borve.demon.co.uk]
Sent: Tuesday, September 17, 2002 4:37 PM
To: 'seqfan at ext.jussieu.fr'
Subject: Re: n^n is interprime

In message <200209171413.g8HED2X23255 at mailgate5.cinetic.de>, Rainer
Rosenthal <r.rosenthal at web.de> writes

>ZAKIRS <zfseidov at ycariel.yosh.ac.il> schrieb am 17.09.02 15:25:28:
>> hallo to all,
>> n^n is interprime for n=2, 6, and 9:
>> 2 is a member because 2^2 = 4 as average of two subsequent primes 3 and
5,
>> 6 is a member because 6^6 = 46656 is average of two subsequent primes 6^6
>> -/+ 7,
>> 9 is a member because 9^9 = 387420489 is average of two subsequent primes
>> 9^9 -/+ 10.
>> Can anybody find next term(s)? thanks, zak
>
>Huh? Isn't 37 prime? I thought so, but ... you are the expert :-)
>
>In case I'm wrong (nothing exceptional), I beg your pardon. The idea is
>very nice anyhow.

3^3 + 10 and 3^3 - 10 are both prime but I think Zak is looking for
cases where n^n sits equidistant from two *consecutive* primes, so 3 is
not in the sequence.

I hope I understood properly! :-)

Zak: what's the largest possible n you've checked for so far?

Best regards,

Neil
--
Neil Fernandez

```