- --- In primenumbers@yahoogroups.com, "djbroadhurst"

<d.broadhurst@...> wrote:

> Definition: A sequence of consecutive positive

My current record is s = 4.1067361598, achieved with

> integers, beginning with N, has strength

> s = log(N)/log(p), where p is the largest prime

> dividing any integer in the sequence.

> Puzzle: Find a sequence of 5 consecutive integers with

> strength s > 3.80.

> I imagine that Jens might soon beat strength s = 4.009147298.

x = 20375617

N = (x^2-3^4)*(x^2-2^10)/55440 = 3108993777544846030873003

David - --- In primenumbers@yahoogroups.com, Andrey Kulsha <Andrey_601@...> wrote:
>

Too hard!

> >> http://www.primefan.ru/stuff/math/maxs.xls

> >> http://www.primefan.ru/stuff/math/maxs_plots.gif

> >

> > Thanks, Andrey. The gradients are fanning out better now:

>

> The files were updated again.

>

> Puzzle: find a chain of 13 consecutive p-smooth integers, starting at N,

> with log(N)/log(p) greater than

>

> log(8559986129664)/log(58393) = 2.71328

>

> Best regards,

>

> Andrey

>

It was difficult getting just over 2 for the first time with

log(287946949)/log(15823).

My only consolation is that the above is also good for 15 consecutive 15823-smooth integers.