20140520, 13:47  #1 
Apr 2014
Marlow, UK
2^{3}·7 Posts 
Distribution of relations over the sieving interval in SIQS
I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1partials and 2partials.
Is this a wellknown phenomena? Could it be used in any way to tune the QS algorithms? Cheers, Mick. 
20140520, 15:22  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3·3,529 Posts 
Quote:
The term "chicken feet" is also relevant, though it may not appear so at first! Last fiddled with by xilman on 20140520 at 15:22 

20140520, 15:26  #3  
"Ben"
Feb 2007
3,371 Posts 
Quote:
Early versions of YAFU tried to take advantage of it, but I don't believe the improvement (if any) amounted to much. It is too expensive to check every 'x' to see if you are close to a root or not. As a compromise I think I put a little more effort into all sieve hits within the block containing the root, but the gain at the root offsets the loss away from the root within the block... Last fiddled with by bsquared on 20140520 at 15:32 

20140520, 15:45  #4 
Apr 2014
Marlow, UK
2^{3}×7 Posts 
Thanks for the replies, guys  interesting.
Mick. 
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