[QUOTE=victor]What about Beal's conjecture?[/QUOTE]

There is no such thing as the Beal Conjecture. There does exist the
Beal PRIZE, which has been offered for the Fermat-Catalan Conjecture,
as sharpened by Tijdeman and Zagier. But Beal's claim of the conjecture
as his own is ridiculous (In my opinion and the opinion of others).

See, for example Pages 416-417 of Crandall & Pomerance.

Read the notice in AMS about beals conjecture.

[QUOTE=R.D. Silverman]the Fermat-Catalan Conjecture, as sharpened by Tijdeman and Zagier.

See, for example Pages 416-417 of Crandall & Pomerance.[/QUOTE]

Or footnote 2 on page 7 here:
[url]http://www.math.jussieu.fr/~miw/articles/pdf/odp.pdf[/url]

[QUOTE=pacionet]Cracking old Enigma ciphered messages here:

[url]http://www.bytereef.org/m4_project.html[/url]

nice ...[/QUOTE]
The project has made the news:

[url]http://news.yahoo.com/s/nf/20060303/bs_nf/41894[/url]

[QUOTE]Krah said that he is not sure the remaining two codes will be cracked. So far, the power of thousands of PCs joined in this effort has resulted in little success. "There is no guarantee that another break will occur at all," Krah was quoted as saying. "There is simply a fair chance."[/QUOTE]

Would a brute force attack be possible? I was wondering this, and how many rotor/plugboard settings a PC could test, in a second.

[QUOTE]The Germans considered the task to be impossible, and certainly even a modern computer might take a year to work through this number of machine settings, if it simply tried them out in turn.
[URL="http://www.codesandciphers.org.uk/enigma/enigma3.htm"]http://www.codesandciphers.org.uk/enigma/enigma3.htm[/URL]
[/QUOTE]

[QUOTE]Would a brute force attack be possible?[/QUOTE]

There are too many possible plug-board configurations.

The second one has been broken:
[url]http://www.bytereef.org/m4-project-second-break.html[/url]

whoa, this project is almost over