- From: Robert ... My immediate gut feel reaction tells me this would be expected. I suspect that my gut feel is wrong though! AsMessage 1 of 4 , Jul 5, 2005View SourceFrom: "Robert" <rw.smith@...>
> In my search for "triple double" values, I am looking for a k, suchMy immediate gut feel reaction tells me this would be expected.
> that the two power series k.2^n+&-1 provide more than 10 Cunningham
> Chains (1st kind), 10 Cunningham Chains (2nd kind) and 10 twins.
> during the search, I have noticed that the number of k's producing
> more than 10 Cunningham Chains length 2 (1st or 2nd kind) tends to
> be consistently higher than the number of k providing 10 twins, and
> the maxima of CCs found also looks to be higher than the maxima for
I suspect that my gut feel is wrong though!
As always, everything should be predicted by sieving with small primes so
look at residues of k*2^n+/-1 mod p for small p, fixed k, variable n.
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- ... CC more common?!? ... Gary: No simple answer to that. I would have to rerun the candidates to find out how many CC3, CC4 etc. My program only countsMessage 2 of 4 , Jul 5, 2005View Source--- In email@example.com, Gary Chaffey <garychaffey2@y...>
> Do the CCs occur in roughly equal numbers or is a particular sort ofCC more common?!?
> GaryGary: No simple answer to that. I would have to rerun the candidates
to find out how many CC3, CC4 etc. My program only counts points.
The statistics for the range of k 1 to 1531174737133 multiplied by
29#/34 (approx 1/20th of the overall numbers checked):
25250 values of k have 7 or more triple double points at n=10
2814 had 13 or more points at n=100 and of these:
81 had 20 or more points at n=500, the best of which were 4 23's and 5
49 of those taken to 500 (2814 candidates)had 10 or more CC's of the
1st kind (including a 13 and 3 12's)
41 of those taken to 500 had 10 or more CCs of the 2nd kind (including
4 of those taken to 500 had 10 or more twins (1 with 11)
1 candidate fell into two categories
As I might have expected, twins are slightly more prevalent - if I
average the scores of the 2814 candidates with 13 or more points, they
have 5.09 CC1s, 5.09 CC2s and 5.25 twins.
So it appears that the distribution curves for CC's amd twins are not
the same, which defies simple analysis.