20060113, 14:17  #243  
Jul 2005
2·193 Posts 
Quote:
I see what you mean about the top end of a range, I'll make a note that these ranges need to be rechecked when we have something that can check them. So far every 3prp number your program has output has been confirmed as prime. However I will always check them with the PARI script to be sure. As for double checking, that is something to bear in mind. Again, I'll add that to my list and have a think about it. P.S. Results for completed ranges posted in a new thread, with downloads. Last fiddled with by Greenbank on 20060113 at 14:18 

20060113, 14:39  #244 
Jun 2003
Oxford, UK
7BE_{16} Posts 
Spiders
I rather like the idea of looking for spiders, with between 0 and 8 legs.
Take an octoproth, this will form the body, with four segments. k*2^n+1,k*2^(n+1)+1 k*2^n1, k*2^(n+1)1 2^n+k, 2^(n+1)+k 2^nk, 2^(n+1)k Now see how many legs the spider has. Each segment has two possible legs, representing n values one less and one more than on the segment. For example: Possible left leg Body Possible right leg k*2^(n1)+1 k*2^n+1, k*2^(n+1)+1 k*2^(n+2)+1 The possible legs become legs when they are prime. A dodecaproth with have four left or 4 right legs, a fully fledged spider will have eight legs. Given that these forms are likely to be highly rare, it would be interesting to see the distribution of legs on those existing octos already discovered. It is highly probable that we will find octos with 4 legs, although they will not all be on one side. 5 legs would be nice. 6 a bonus although unlucky. Regards Robert Smith 
20060113, 15:01  #245 
Jul 2005
2×193 Posts 
n=51 is complete and has 16870 confirmed Octoproths. Will add this to the info and downloads shortly.

20060113, 15:31  #246  
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 
Quote:
See post 65  69 of this tread. 

20060113, 15:51  #247  
Jul 2005
2·193 Posts 
Quote:
axn1's program still outputs those values, otherwise Templus would not know them to pass them through PFGW. octo 4.5 (and previous versions) does not even output these values as possible octoproths. And yes, Templus forgot to add the last 4 cases to the ABC line. 

20060113, 15:58  #248 
"Robert Gerbicz"
Oct 2005
Hungary
7^{2}×31 Posts 
Greenbank can you modify the function of f=floor() to f=round(), see the number of octoproth thread, because in this case it'll give also that for n<27: f(n)=0 and for n>=27 : f(n)>0
ps in some cases it'll give the correct number of octoproths!!! 
20060113, 17:15  #249  
Jun 2003
5·1,039 Posts 
Quote:
Last fiddled with by axn on 20060113 at 17:18 

20060113, 17:16  #250  
Jun 2003
5×1,039 Posts 
Quote:
Last fiddled with by axn on 20060113 at 17:17 

20060113, 17:31  #251  
"Robert Gerbicz"
Oct 2005
Hungary
5EF_{16} Posts 
Quote:


20060113, 17:59  #252 
Jun 2003
Oxford, UK
11110111110_{2} Posts 
32
32 was the first number I checked, and I went up to k=4bn, using NewPgen as the initial sieve, and pfgw for primality testing, and only found 6, so that the 3762658725 value was not amongst those  see message #1 in this thread!!
Regards Robert Smith 
20060113, 18:19  #253  
Jun 2003
5·1,039 Posts 
Quote:
Blame it on human error. The primality testing was a manual process. I tried to be careful but somehow this one has slipped thru Anyway, the important thing about that post was the last bit  i.e. no Octos in [2^n10^5,2^n2] for n <= 64. Last fiddled with by axn on 20060113 at 18:20 

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