20140512, 21:04  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
19·491 Posts 
Leyland Primes (x^y+y^x primes)
Placeholder for x^{y}+y^{x} prime search reservations.
Contact XYYXF to reserve a range. Multisieve is one of the sieve programs capable of sieving this form. Last fiddled with by XYYXF on 20150202 at 15:03 
20140513, 13:09  #2 
Jun 2012
2961_{10} Posts 
Yafu can sieve this form too.

20140513, 13:45  #3 
"Ben"
Feb 2007
3,371 Posts 
It can?

20140513, 14:12  #4 
Romulan Interpreter
Jun 2011
Thailand
9275_{10} Posts 
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. Last fiddled with by LaurV on 20140513 at 14:14 
20140513, 14:17  #5 
Jun 2012
3^{2}·7·47 Posts 

20140513, 14:46  #6 
"Ben"
Feb 2007
6453_{8} Posts 

20140513, 17:54  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
19·491 Posts 
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.
A worked example: 1. Get Multisieve 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 1020s per candidate) 4. Run pfgw on the "xyyx200.out" file (with f0 l) 5. ... 6. PROFIT! e.g. 200^20373+20373^200 is a (new) PRP 7. Submit to PRP top 
20140513, 19:01  #8 
Jan 2005
Minsk, Belarus
620_{8} Posts 

20140513, 19:08  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
19·491 Posts 
Multisieve reversed that order (because x^{y} > y^{x}, for 3<=x<y, and because it sieves for x^{y} +/ y^{x}, 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 [2000140000, 11200] range. Found six new PRPs so far, while warming up. 
20140513, 19:19  #10 
Jan 2005
Minsk, Belarus
2^{4}·5^{2} Posts 
OK, http://xyyxf.at.tut.by/primes.html#ranges 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 [1500120000, 10012000]. 
20140513, 22:28  #11 
"Mark"
Apr 2003
Between here and the
1100001100101_{2} Posts 
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.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Leyland Primes: ECPP proofs  Batalov  XYYXF Project  16  20190804 00:32 
Mersenne Primes p which are in a set of twin primes is finite?  carpetpool  Miscellaneous Math  3  20170810 13:47 
Distribution of Mersenne primes before and after couples of primes found  emily  Math  34  20170716 18:44 
On Leyland Primes  davar55  Puzzles  9  20160315 20:55 
possible primes (real primes & poss.prime products)  troels munkner  Miscellaneous Math  4  20060602 08:35 