20220703, 14:51  #1  
Random Account
Aug 2009
Not U. + S.A.
100111100100_{2} Posts 
Leyland Primes
Member pxp has a data table of Leyland primes here. I decided to do an experiment based on two items in his table. Lines 519 and 521. (6255,1496) and (6312,1427). I created a sieve within the rules of what rogue's xyyxsieve program would allow. I ran the results with OpenPFGW. I wasn't expecting to find anything, but I did. The below took about 18 hours of run time. I stopped the process at this point.
Quote:


20220703, 15:13  #2  
Sep 2002
Database er0rr
2^{3}·3·11·17 Posts 
Quote:
A number n being Fermat 3PRP means 3^(n1)==1 mod n. Due to fast leftright exponentiation and for large numbers using FFT further speeds up testing. But is is not 100%. For this we need some other method of proof. If we can get just over 25% factorization of n1 and n+1, there are quick methods akin in speed to a PRP test. If no easy method is to be had then we have to use something like ECPP which uses the arithmetic of elliptic curves. The most recent incarnation is Andreas Enge's CM program. A PRP test might take minutes on a single core, whereas ECPP might take weeks on a multicore system. I think why your found numbers are not in pxp's table is that they are not of the form x^y+y^x. Last fiddled with by paulunderwood on 20220703 at 15:26 

20220703, 17:18  #4  
Random Account
Aug 2009
Not U. + S.A.
2^{2}·3·211 Posts 
Quote:
I didn't know Leylands were "+" only. I should have paid more attention. It is even in the topic title. Quote:
I changed the sign in my sieve to "+" and sieved to P = 50,000,000. Instead of having thousands of candidates, there were only 90. 

20220703, 19:40  #5  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·3·29·67 Posts 
Quote:
It works just as well (exactly the same, in fact) under Windows, MacOS, BSD and anything else to which the GMP library has been ported. The only reason I have not yet run it under Windows is that I haven't yet bothered to try. I plead guilty to the charge of laziness. That that you didn't see anything says much more about your observational ability than anything else. 

20220703, 23:47  #6 
Random Account
Aug 2009
Not U. + S.A.
2^{2}×3×211 Posts 
Everything I saw was "tar" and/or "gz." I will have to look again. My observational ability is far less than it used to be. I won't say more because I have already been belittled for it once. I may have to quit on all this in a year or so.

20220704, 14:32  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·3·29·67 Posts 
Quote:
Windows has been able to read them for over twenty years to my knowledge  back when I worked for MSFT. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Leyland Primes (x^y+y^x primes)  Batalov  XYYXF Project  610  20230201 10:00 
Leyland Primes: ECPP proofs  Batalov  XYYXF Project  57  20220630 17:24 
3 as Leyland prime?  JeppeSN  XYYXF Project  2  20200817 09:26 
On Leyland Primes  davar55  Puzzles  9  20160315 20:55 
Leyland Numbers  Numberphile  TimSorbet  Lounge  5  20141029 07:28 