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-   -   Leyland Primes (x^y+y^x primes) (https://www.mersenneforum.org/showthread.php?t=19347)

 Batalov 2014-05-12 21:04

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.

 swellman 2014-05-13 13:09

Yafu can sieve this form too.

 bsquared 2014-05-13 13:45

It can? :ermm:

 LaurV 2014-05-13 14:12

: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.

 swellman 2014-05-13 14:17

[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.

 bsquared 2014-05-13 14:46

[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.

 Batalov 2014-05-13 17:54

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]:
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]

 XYYXF 2014-05-13 19:01

[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 :-)

 Batalov 2014-05-13 19:08

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.

 XYYXF 2014-05-13 19:19

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].

 rogue 2014-05-13 22:28

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.

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