20200622, 19:57  #342 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10000010110011_{2} Posts 
Just for safety I am dropping a snapshot of that file here as a zip.

20200622, 22:10  #343 
"Mark"
Apr 2003
Between here and the
5844_{10} Posts 
This page, http://www.primefan.ru/xyyxf/primes.html#0, is not being updated. Where is the status of the search being maintained?
Is there a table with a list of all ranges that have been checked, who checked them, and when? I'm asking because if someone wants to participate, they would have difficulty knowing where to start. 
20200623, 12:35  #344  
Sep 2010
Weston, Ontario
150_{10} Posts 
Quote:
Still, one can say that once we have reached 81300 digits, x needs to be greater than 19000, or when we have reached 86025 digits, x needs to be greater than 20000, and so on. If my indexing effort reaches 105130 digits (which seems doable by 2022), x will need to be greater than 24000. That would be one thing to keep in mind if one wishes to participate. A second thing is that for larger x up to 50000, y has supposedly been checked up to 800. For larger x up to 500000, y has supposedly been checked up to 25. Just pick something. There's unlikely to be any duplication. If you know how to sort (x,y) pairs by L(x,y) digitsize, even better. You can pick a range of digitsizes and contribute what you find. If you really want a challenge, find the nextlarger PRP after Serge Batalov's L(328574,15). It will immediately become the largestknown Leyland prime. 

20200623, 13:59  #345  
"Mark"
Apr 2003
Between here and the
2^{2}×3×487 Posts 
Quote:
Are you saying that once you reach x = 19000 that all y < x have been searched for those x? Is the intention to "not trust" what others have done and just retest all y < x for the range of x? The table at the top of http://www.primefan.ru/xyyxf/primes.html#0 is really useful, but is useless since it is out of date. Why can't you just have a copy of that on your page and keep it up to date? It shouldn't be hard unless you are purely focused on "decimal length" as your goals instead of the goals of the original project. If you are focused purely on "decimal length" goals does that mean that for each x you are searching to a different y? If so, are you even using xyyxsieve? Are you sieving then manipulating the output to "skip" x/y values larger than the decimal length you are searching for? 

20200623, 22:06  #346 
Sep 2010
Weston, Ontario
2·3·5^{2} Posts 
For me this all started in April 2015 when I computed a table of the first 5000 Leyland numbers (OEIS A076980). At the same time I realized that I could do something similar with the Leyland primes and thus contributed a table of the first 100 Leyland primes (OEIS A094133). I wondered how many of the then1092 known Leyland primes were indexable and thus I extended my prior calculation of the first 100 Leyland primes to the first 954 Leyland primes. In May 2015 I used my result to curvefit the Leyland number indices of those 954 Leyland primes and determined that the largestknown Leyland prime L(328574,15) would have a Leyland prime index of ~5550. That meant that there were thousands of smaller Leyland primes waiting to be discovered. It also meant that because everyone was so focused on this x/y reservation scheme, I might be able to find new, relativelysmall primes by examining the Leyland numbers between existing Leyland primes. Thus began my Leyland prime hunt.
The basis of the hunt was my creation of a database of the first 331682621 Leyland numbers. That would include all Leyland numbers up to 100000 digits. They were represented as (x,y) pairs and sorted by L(x,y) size. I would step through these pairs in Mathematica one at a time, testing each one for GCD[x,y]==1 before doing PrimeQ[L(x,y)]. That's it. No sieving and I never worry about where the x or the y are at. Yes, that's important when one is distributing a computation and need to keep track of who is doing what. I just never bought into that since I was pursuing my own goal of indexing the Leyland primes. And to that extent I feel good about what I have accomplished. Those initial 954 indexed primes are now 1567 indexed primes. Of those 613 added indices, 422 are for primes that I have discovered. I knew when I started this project that I might be stepping on some toes and for that I apologize. On the other hand, as I have tried to point out, there is nothing preventing folk from stepping out of their comfort zone and continuing the dance to a new beat. 
20200624, 02:31  #347 
"Mark"
Apr 2003
Between here and the
1011011010100_{2} Posts 
Then the original search and yours are like comparing apples to oranges.
If someone wants to work on ranges for the original project, but not redo your work, then would have difficulty knowing where to start. If you are not sieving, then you are probably wasting a ton of time trial factoring and PRP testing. What you can do is sieve with xyyxsieve, then use a script to pare done the terms that are outside of the decimal length you are searching. 
20200624, 11:08  #348 
Sep 2010
Weston, Ontario
2·3·5^{2} Posts 
The idea of using a script already makes it unlikely that xyyxsieve would be a fit for my lack of programming skills (I've used Mathematica for 24 years and I still have to regularly look stuff up). Are you saying that if I wanted to search for Leyland primes from just above Serge Batalov's L(328574,15) to, say, L(80332,71590) [64138108 Leyland numbers that run from 386434 digits to 390000 digits; I have a 1 GB text file of the sizesorted (x,y) pairs] I would first have to use xyyxsieve to cull candidates from all Leyland numbers up to some incredibly large term and then throw out the ones that are less than 386434 digits or more than 390000 digits? How does one feed xyyxsieve so that it is guaranteed to include every Leyland number candidate in that range? What might be the memory requirement to do that?

20200624, 12:27  #349  
"Mark"
Apr 2003
Between here and the
2^{2}·3·487 Posts 
Quote:
Assuming you have multiple cores for testing, I suggest that you set up a PRPNet server. Once a server is set up this is by far the fastest way to distribute work across multiple cores and multiple computers. You don't need programming skill to run PRPNet. You will need to install MySQL or PostgreSQL and create a database. I can help you with that. It isn't as hard as you might think. 

20200626, 18:34  #350 
Sep 2010
Weston, Ontario
150_{10} Posts 
If this is just a matter of finding terms that I want to test, I can and have already done that in Mathematica. For example, there are only 17632 Leyland numbers greater than Serge Batalov's L(328574,15) that have exactly 386434 decimal digits. Selecting those that have GCD(x,y) = 1 reduces this to 10808 terms. Subjecting these numbers to Mathematica's PrimeQ (which is Mathematica's PRP test) for at most one second per term reduces our candidate list to 1324 terms. PrimeQ has a builtin smallprimes divisor test and I think one second per term is enough to run that part of it. Still, that requires about 4 minutes on my old 2013 Mac and I've been reluctant to apply it to the entire database of 64138108 Leyland numbers (386434 digits to 390000 digits). I did however create similar lists of 386435digit terms and 386436digit terms just as a proof of concept. The nice thing about the lists is that the entries are ordered by L(x,y) magnitude (every term is larger than its immediate predecessor).
For me the hard part is actually doing a full PRP test on the numbers. PrimeQ[L(85085,34812)] took over 6 hours on my main machine, albeit all 4 of its cores are busy on another project. I would not be surprised that there is software that can do this much faster. But lacking such, it would take me 11 months to test the entire first list. If my Macmini farm weren't already engaged, I could do it in a week. But that is one list. There will be 3567 such lists to get up to 390000 digits. 
20200626, 18:56  #351  
Bamboozled!
May 2003
Down not across
10,159 Posts 
Quote:
Unfortunately I am busy factoring Generalized Cullen and Woodall numbers. Just one of those is expected to take me more than a year unless others help me. I no longer have the cpu power that I used to have. 

20200626, 20:14  #352 
"Mark"
Apr 2003
Between here and the
2^{2}×3×487 Posts 
pfgw will likely be faster since it is based upon the gwnum library. I suggest that you run and compare to the PrimeQ function of Mathematica. I do not have Mathematica, so I cannot compare its speed with pfgw. Since I have 2013 MacBook Pro, I'm guessing that pfgw is about 2x faster than Mathematica, given the information you have when using PrimeQ.
I'll make you an offer. Send me one of your lists and I'll sieve with xyyxsieve. I'll sieve to the appropriate depth and send the list back to you. That way both of us can see how much time it could save your project. If there is overlap between x and or y in the lists, send me all of your lists and I can see how xyyxsieve handles doing it all in one chunk. Last fiddled with by rogue on 20200626 at 20:15 
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