- --- In primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:
>

Pure chance.

> Let x = sqrt(3) + sqrt(2).

>

> Then (x^n + 1/x^n)/(2*sqrt(3)) is prime (or PRP) for

>

> n = 5, 7, 13, 107, 227, 491, 8009, 36779 ...

>

> while (x^n - 1/x^n)/(2*sqrt(2)) is prime (or PRP) for

>

> n = 3, 5, 37, 41, 43, 59, 71, 113, 181, 293, 383, 421,

> 1109, 1187, 1997, 3109, 4889, 5581 ...

>

> Puzzle: Why is the second Lehmer series more fertile at small n?

I have some experimental evidence for this, which shall be posted tomorrow.

Mike - --- In primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:
>

Congrats! That size of 15537 digits is nearly 25% bigger than the next 12 on that "Top-20" Lehmer Primitive Part list, which all date from more than 3 years ago. So, a massive improvement!

> --- In primenumbers@yahoogroups.com,

> "David Broadhurst" <d.broadhurst@> wrote:

>

> > The Society for Suppression of Square Roots hopes to

> > be able to announce, within a few days, the proof of

> > a unique Lehmer prime with more than 15000 digits

> > (wenn die Frau GĂ¶ttin probiert hat).

> > If proven, it will also become the largest known prime at

> > http://primes.utm.edu/top20/page.php?id=68

>

> Consummatus est in brevi explevit tempora multa [Wisdom:4:13]

>

> http://primes.utm.edu/primes/page.php?id=88162#comments

Mike