20081115, 12:46  #111 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
1011110001111_{2} Posts 
Reserving 650660M (to 25k)

20081115, 23:04  #112  
"Gary"
May 2007
Overland Park, KS
2×5×1,181 Posts 
Quote:
It is false. No k in base 3 should have algebraic factors such that the k could be eliminated that I am aware of. Let me define "having" algebraic factors such that the k could be elimianted without a prime being found: Having algebraic factors means that a k has such factors that COMBINE with numeric factors to make a FULL covering set and hence eliminate a kvalue from consideration. k=510669604 is a perfect square. Like any other k that is a perfect square, it has algebraic factors for all even n. BUT...it still must be searched for all odd n. There is no covering set for the odd n. Here are the factors for the first few small oddn: Code:
n factors 1 1201*1275611 3 23*61*9827569 5 13*71*83*877*1847 7 11*101530402177 9 2402353*4184027 510669604*3^551 = 7,976,141,243,627*11,169,048,639,317,939,512,801 This clearly demonstrates that there is no pattern of any kind of covering set of numeric or algebraic factors on the odd n. It should eventually yield a prime. Editor note (lol): 510669604*3^10651 is prime! Gary Last fiddled with by gd_barnes on 20081117 at 05:18 Reason: found prime 

20081115, 23:18  #113  
"Gary"
May 2007
Overland Park, KS
2×5×1,181 Posts 
Quote:
I just got a bunch of primes from for what appears to be k=500M510M/n=1K6.2K and k=500M502M/n=6.2K25K. Micha, have you tested k=502M510M for n=6.2K25K yet? Kenneth, since you're doing this, starting with my next update of my web pages, I'm going to just link to your website for k's remaining and reservations. Are you OK with that? We can both manage the remaining minidrive I. I'll move it over to your subforum. As for k's remaining, you'll need to do what I've been doing...that is make sure no extra k's are left in as a result of multiples of the base whenver anyone sends you a group of k's that are remaining. You've been highly accurate in sending them to me the last 2 times so clearly you understand how to verify it. Gary Last fiddled with by gd_barnes on 20081116 at 03:10 

20081115, 23:42  #114  
"Gary"
May 2007
Overland Park, KS
2×5×1,181 Posts 
Quote:
Micha, There are 2 problems here: 1. It is extremely highly unlikely that there are only 4 k's remaining in a k=10M range. I will go so far as to say that it's virtually impossible. What range have you tested? This might be reasonable for k=500M502M. I see that all k's remaining are in that range. Upon testing k<10M to n=60K, we still have 10 k's remaining and at least 23 k's were eliminated with primes for n>100K! As you know the k's remaining will generally be higher for the same krange as the k's get higher since the numbers are higher so the possibility of only 4 k's remaining at n=25K is even smaller for k=500M510M than for k<10M. 2. There are 2 k's here that shouldn't be remaining. I'll see if you guys can find them. Edit: I just now looked at your 2nd primes file for n=6.2K25K. It only contains primes for k=500M502M. Therefore, I believe what I stated in #1 is correct. You have only listed k's remaining for k=500M502M. Are you testing KEP here? lol Gary Last fiddled with by gd_barnes on 20081116 at 00:06 

20081116, 09:35  #115  
Quasi Admin Thing
May 2005
3D6_{16} Posts 
Quote:
Kenneth. 

20081116, 10:30  #116  
Jan 2005
1DF_{16} Posts 
Quote:
I _though_ I did 500 to 510 :) I _think_ I buggered up someplace... I _know_ I'll do them again, and be careful now... 

20081116, 10:36  #117 
Jan 2005
479_{10} Posts 

20081116, 15:24  #118  
Quasi Admin Thing
May 2005
2×491 Posts 
Quote:
Thanks for redoing the range, because as Gary states, this result is likely to be false and erroneous since more k's should remain. In average 45 k's should remain per 1M range, before removal of redundant k's. At least this has been the average per 1M range for k<=250M. KEP 

20081117, 17:21  #119 
I quite division it
"Chris"
Feb 2005
England
31·67 Posts 
510520M complete.
4,997,762 primes with n <= 1000. 8 tiny PRPs that proved to be not prime but were found slightly higher (all had n of 2 or 3). 2,167 primes with n > 1000. 63 remaining Ks for Kep to fiddle with. 5,000,000 total. Remaining Ks to be sent to Kep. All primes to be sent to Gary. Let's see if we can fill up his hard drive! 
20081119, 12:52  #121  
"Gary"
May 2007
Overland Park, KS
27042_{8} Posts 
Quote:
That may take a while: I have a 360 GB autobackup drive affectionally referred to as "The book" by the computer store that I got it from 2 months ago. Good luck filling THAT up! Perhaps if you sent me all primes for n>10 for all k up to 63G! (lol) The drive cost ~$80. If you guys somehow fill it up, you get to buy me another one! hehehe The largest space being used for results is (surprisingly) NOT by NPLB nor by base 3 (YET!), it is for my "all" twin prime search, which is currently stalled in the n=50K range for all k<1M. At about 600700 tests per nvalue at a sievedepth of P=60G, the results for it are eating a large chunk of one of my 2 GB flash drives right now. Once they pass about 1.5 GB, I'll have to dump it to the book. Edit: I just checked my Email. Chris, you don't need to send me primes for n<1000. Yes, you would fill up the book with THAT! Kenneth, weren't you telling people to just send me primes for n>1000? I think we agreed that we can quickly reconstruct primes n<1000 when it is needed. I'm only going to save off the primes to my hard drive that were sent for n>1000. I won't delete the Email until later. Gary Last fiddled with by gd_barnes on 20081119 at 12:57 

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