mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > And now for something completely different

Reply
 
Thread Tools
Old 2020-03-29, 22:57   #1
sweety439
 
sweety439's Avatar
 
Nov 2016

215910 Posts
Default Carol / Kynea half squares

Quote:
Originally Posted by rogue View Post
I've decided to start a new thread for a coordinated Carol / Kynea search. Carol and Kynea primes are subset of what is known as Near Square Primes. These primes have the form of (b^n-1)^2-2 (Carol) and (b^n+1)^2-2 (Kynea). Steven Harvey has coordinated the search in the past and still coordinates the base 2 search here. This thread is for those who want to search other bases. Although his page has some other bases on it, the page is incomplete and it is unknown to me if there are any gaps or if bugs might have causes previous searches to miss some primes.

I am already working on base 2 in another thread of the sub-forum and am coordinating that effort with Steven directly.

Odd bases can be skipped because the Carol/Kynea number is always even. I could modify the sieve to test (b^n+/-2)^2+/-1 for odd b, but that is for a different project somewhere down the road.

pfgw (for base 2) is about 15% faster than llr, so pfgw is recommended for testing this form at this time.
This form is supported by PRPNet, so you can find that elsewhere if you want to use it to distribute PRP testing.

Please post primes in this thread.

Please go here to see a list of current reservations and to find the current version of cksieve, but continue to use this thread to submit and complete your reservations.

Attached are sieving files available for testing. You may want to verify that they have been sufficiently sieved before beginning testing.
For odd b, I suggest ((b^n-1)^2-2)/2 (Carol) and ((b^n+1)^2-2)/2 (Kynea), they are half Carol/Kynea, like the generalized half Fermat.
sweety439 is offline   Reply With Quote
Old 2020-03-29, 22:59   #2
sweety439
 
sweety439's Avatar
 
Nov 2016

1000011011112 Posts
Default

Quote:
Originally Posted by sweety439 View Post
For odd b, I suggest ((b^n-1)^2-2)/2 (Carol) and ((b^n+1)^2-2)/2 (Kynea), they are half Carol/Kynea, like the generalized half Fermat.
These are status for both sides for b<=512, searched up to n=1024
Attached Files
File Type: txt Carol for b le 512.txt (9.9 KB, 26 views)
File Type: txt Kynea for b le 512.txt (10.1 KB, 14 views)
sweety439 is offline   Reply With Quote
Old 2020-03-29, 23:01   #3
sweety439
 
sweety439's Avatar
 
Nov 2016

41578 Posts
Default

Can someone find a prime of the form ((81^n-1)^2-2)/2, ((215^n-1)^2-2)/2, ((319^n-1)^2-2)/2, ((73^n+1)^2-2)/2, ((109^n+1)^2-2)/2, ((205^n+1)^2-2)/2, etc?
sweety439 is offline   Reply With Quote
Old 2020-03-29, 23:41   #4
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23·5·227 Posts
Default

It is very easy.

((205^3651+1)^2-2)/2
((205^4133+1)^2-2)/2
((205^4620+1)^2-2)/2
((215^12694-1)^2-2)/2
((319^11276-1)^2-2)/2
((319^5513-1)^2-2)/2
((73^1275+1)^2-2)/2
((73^2004+1)^2-2)/2
etc


However, the problem with these half-near-squares is that you will not be able to prove (most of) them. (Take these PRP-1 and PRP+1: there is nothing immediately smooth about them.)
Batalov is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Carol / Kynea Primes rogue And now for something completely different 239 2020-08-03 06:58
Carol / Kynea Coordinated Search - Reservations rogue And now for something completely different 257 2020-06-20 03:13
Carol / Kynea search (Near-power primes) rogue And now for something completely different 37 2016-06-18 17:58
a 18+ Christmas carol science_man_88 Lounge 10 2010-12-13 23:26
TF: A job half done? davieddy Lounge 35 2010-10-01 20:18

All times are UTC. The time now is 12:06.

Mon Aug 10 12:06:34 UTC 2020 up 24 days, 7:53, 3 users, load averages: 1.74, 1.77, 1.74

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.