Re: [PrimeNumbers] Re: The house that Jack built

Expand Messages
• ... Fewer even numbers? Phil
Message 1 of 69 , Mar 25, 2009
> 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?

Fewer even numbers?

Phil
• ... 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
Message 69 of 69 , May 10, 2009
>
>
> > 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]
>