Re: Lucas super-pseudoprime puzzle
- --- In firstname.lastname@example.org,
"mikeoakes2" <mikeoakes2@...> wrote:
>> n is a solution if and only if it is an oddYes. So far I have run the faster test up to n = 9*10^9.
>> square-free composite integer such that for each prime p|n
>> n = +/- 1 mod p-1 ... 
>> n = +/- 1 mod p+1 ... 
> It might be interesting to program this test as it might be
> significantly faster for large n, not so?
Confirmation of the claim that the next solution has
n > 10^10 should not take much longer.
I did not see Jacobs, Rayes and Trevisan remark
on the fact that n cannot be divisible 3, so
please pat yourself on the back, Mike.
- --- In email@example.com, "djbroadhurst" <d.broadhurst@...> wrote:
>You did very much what I did.
> I tried 1/n^c:
> v=[1237.1, 328.7, 105.4, 28.01, 6.22 , 1.510, 0.439, 0.0939];
> [0.5815, 0.5805, 0.5682, 0.5691, 0.5785, 0.5821, 0.5780, 0.5856]
> and then A/n^c, using the first datum to remove A:
> [0.5756, 0.5348, 0.5484, 0.5747, 0.5827, 0.5750, 0.5885]
> In both cases c =~ Euler looks rather convincing,
> given the statistics. Well spotted, Sir!
I nearly fell off the chair when I averaged everything out and saw 0.57... :-)
> How strongly are you committed to A = 1, for the average,Not very.
> given the variability of the overall factor with a?
Would you buy an appeal to Occam's razor, mon vieux?