Leyland Primes (x^y+y^x primes)
 

Placeholder for x[SUP]y[/SUP]+y[SUP]x[/SUP] prime search reservations.

Contact [URL="http://www.mersenneforum.org/member.php?u=1540"]XYYXF[/URL] to [URL="http://www.primefan.ru/xyyxf/primes.html#0"]reserve a range[/URL]. Multisieve is one of the sieve programs capable of sieving this form.

Yafu can sieve this form too.

It can? :ermm:

:missingteeth::ick:

Sorry, I don't laugh at any of you. It is just about the situation, I expected all in the world but didn't expect Ben's reply to this, in this way! [edit: if some guest read this, maybe they don't know, Ben is yafu's author].

I can't stop laughing.

[QUOTE=bsquared;373350]It can? :ermm:[/QUOTE]

You mean it can't? I thought Yafu did everything. :smile:

I stand corrected - Yafu can factor this form via SNFS.

[QUOTE=swellman;373354]You mean it can't? I thought Yafu did everything. :smile:

I stand corrected - Yafu can factor this form via SNFS.[/QUOTE]

Err, well, yes, of course it can do everything, except for LaurV's loops and ifs :smile:

Yep, you were probably thinking of SNFS factorization.

Well, of course, sieving can be done with almost any program (including your own). But the question is how fast can it sieve. Multisieve is good.

[U]A worked example[/U]:
1. Get [URL="http://home.roadrunner.com/~mrodenkirch/home/MultiSieve.html"]Multisieve[/URL] and PFGW
2. Start, select x^y+-y^x mode, select "+", set up some names for outputs, e.g. "xyyx200.out" and "xyyx200.log"; set up limits above previously searched: e.g. x from 200 to 200, y from 20001 to 30000
3. Sieve, after a while, stop (e.g. at 10-20s per candidate)
4. Run pfgw on the "xyyx200.out" file (with -f0 -l)
5. ...
6. PROFIT! [SPOILER]e.g. 200^20373+20373^200 is a (new) PRP[/SPOILER]
7. Submit to [URL="http://www.primenumbers.net/prptop/submit.php"]PRP top[/URL]

[QUOTE=Batalov;373363]e.g. x from 200 to 200, y from 20001 to 30000[/QUOTE]Conventionally x is always greater than y, and it's also recommended to test all y's for a given x :)

So it's better to take e.g. x from 12501 to 13000, y from 2001 to 12999 :-)

Multisieve reversed that order (because x[SUP]y[/SUP] > y[SUP]x[/SUP], for 3<=x<y, and because it sieves for x[SUP]y[/SUP] +/- y[SUP]x[/SUP], so it would be convenient to have a positive number). It was an example of setting up Multisieve. Multisieve will require x<y.

Let's start the fun?
I will run the [20001-40000, 11-200] range. Found six new PRPs so far, while warming up.

OK, [url]http://xyyxf.at.tut.by/primes.html#ranges[/url] is updated. But I still hope someone will decrease the number of steps y>10, y>200, y>1000, y>2000 :-)

E.g. it's possible to take [15001-20000, 1001-2000].

I haven't touched MultiSieve in years. It's good to know that some people still have use for it. After looking at the code (talk about a blast from the past), I think it would be easy to convert this sieve to OpenCL since it doesn't use a discrete log. An OpenCL version might 100x faster.