All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Nickki Primes (Posted on 2011-10-18) Difficulty: 4 of 5

x^4+1 is prime for {2, 17, 257, 1297, 65537, 160001..} (A037896 in Sloane - see also A077497 in Sloane.) Now 160001 is 2^8*5^4+1, equivalently 2*4*10^4+1, and the same series A037896 includes both 40960001 and 655360001.

Call such prime numbers, of the form 2^(4k)*10^(4n)+1, where either or both of (4k+1) and (4n+1) are also prime, Nickki primes.

There are then 3 kinds of such primes:
(4k+1) prime, (4n+1) composite: 1st kind.
(4k+1) composite, (4n+1) prime: 2nd kind
(4k+1) prime, (4n+1) prime: 3rd kind

1. It is not hard to find Nickki primes of the 3rd kind for qualifying k up to 7, but are there any more such primes for, say, k not exceeding 25?

2. {k=5, n=1} is an example of a Nickki prime of the 2nd kind. Are there any others for, say, k not exceeding 25?

3. [harder] Is there a Nickki prime of either the 1st or 3rd kind for every qualifying k not exceeding 25?

No Solution Yet Submitted by broll    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips A resource Comment 1 of 1

This link may help you to get started:

  Posted by broll on 2011-10-21 22:46:02
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information