- Indeed, this is a remarkable discovery!Congratulations for the finding.

--- On Thu, 2/11/10, Chris Caldwell <caldwell@...> wrote:

From: Chris Caldwell <caldwell@...>

Subject: RE: [PrimeNumbers] First known prime factor of Fermat number F14

To: primenumbers@yahoogroups.com

Date: Thursday, February 11, 2010, 8:43 PM

To add some context: F_14 = 2^(2^14)+1 was shown to be composite in

1963 by John Selfridge and Alexander Hurwitz. It took two-score and

seven years to actually find a factor. (This factor by Rajala and

Woltman is the first known factor; and the cofactor is composite.)

F_12 is the smallest Fermat with an incomplete factorization and F_20 is

the smallest with no known factor.

Happy factoring!

-----Original Message-----

From: primenumbers@ yahoogroups. com [mailto:primenumbers@ yahoogroups. com]

On Behalf Of alpertron

Sent: Thursday, February 11, 2010 11:50 AM

To: primenumbers@ yahoogroups. com

Subject: [PrimeNumbers] First known prime factor of Fermat number F14

Tapio Rajula posted a few days ago in

http://www.mersenne forum.org/ showthread. php?t=13051

<http://www.mersenne forum.org/ showthread. php?t=13051> (Mersenne forum)

that he found a prime factor of F14:

1169280858730743698 2903599383459637 1340386703423373 313

Best regards,

Dario Alpern

[Non-text portions of this message have been removed]

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[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com,

"alpertron" <alpertron@...> wrote:

> a prime factor of F14:

Thanks, Dario, for communicating Tapio Rajala's grand discovery.

> 116928085873074369829035993834596371340386703423373313

I remark that http://www.prothsearch.net/fermat.html

is still consistent with the (to me, quite bizarre)

conjecture that omega(2^(2^n)+1) is a non-decreasing

function of n.

Can anyone please tell me who dreamed up that still

unfalsified conjecture? More importantly, was there ever the

remotest hint of an heuristic argument? Or was this merely

blatant exploitation of the law of small numbers?

Best regards

David Broadhurst