[seqfan] Re: n^n + prime(n) = k^k

[Frank Adams-Watters]

OK, presumably you means n^2 + prime(n) = k^2.

Algebraically, this is k^2 - n^2 = (k + n) * (k - n) = prime(n).
For (k + n) * (k - n) to be prime, we must have k - n = 1 (otherwise 
this is a factorization.

But for n>6, prime(n) > 2*n + 1.

So there are no other solutions.

Franklin T. Adams-Watters

-----Original Message-----
From: Frank Adams-Watters <franktaw at netscape.net>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Mon, Jul 21, 2014 3:58 pm
Subject: [seqfan] Re: n^n + prime(n) = k^k


Say what?

5^5 = 3125, fifth prime = 11, total 3136.
6^6 = 46656.

Franklin T. Adams-Watters

-----Original Message-----
From: юрий гераси
 мов <2stepan at rambler.ru>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Mon, Jul 21, 2014 3:31 pm
Subject: [seqfan] n^n + prime(n) = k^k




Dear SeqFans,
n^n + n-th prime = k^k:
1) 5^5 + 5-the prime = 6^6;
2) 6^6  +  6-the prime = 7^7;
3) ?
JSG.

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