- --- In primenumbers@yahoogroups.com,

"mikeoakes2" <mikeoakes2@...> wrote:

>> n is a solution if and only if it is an odd

Yes. 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 ... [1]

>> n = +/- 1 mod p+1 ... [2]

> 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.

David - --- In primenumbers@yahoogroups.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];

> print(vector(8,k,-log(v[k]/10^6)/(k+4)/log(10)));

>

> [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:

>

> print(vector(7,k,-log(v[k+1]/v[1])/k/log(10)));

>

> [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?

Mike