Mathematical Highlights of 2005
 

The end of the year is upon us and I thought it would be interesting to have a list of the most interesting accomplishments in the world of mathematics for the year of 2005. I will start the list with the two Mersenne primes that were found this year.

Two primes for PSP as well

[QUOTE=rogue]The end of the year is upon us and I thought it would be interesting to have a list of the most interesting accomplishments in the world of mathematics for the year of 2005. I will start the list with the two Mersenne primes that were found this year.[/QUOTE]Not only was the first prime factor with at least 60 digits found this year, several of them were.


Paul

For me, the most [b]interesting[/b] result was when SHA-1 was broken.

Maybe not the most significant result, but I do find it very interesting.

RSA-640 was factored .

[QUOTE=xilman]Not only was the first prime factor with at least 60 digits found this year, several of them were.[/QUOTE]With ECM of course :wink:

AMG64 gaining a strong foothold in the marketplace. The fast 64x64->128 bit product was key to the latest ECM successes. All the p60+ were found on Opterons!

Alex

Edit: Gah - not much of a [U]mathematical[/U] achievement, is it? Missed that...

[QUOTE=akruppa]AMG64 (sic!) gaining a strong foothold in the marketplace.[/QUOTE]


Thinking about a new Mercedes? :lol:

On-Topic:
As many important events have already been mentioned, I add the prime of SoB - and gmp-ecm 6.0! :banana: :bow:

[QUOTE=smh]With ECM of course :wink:[/QUOTE]Thanks. I posted that in a great hurry --- too much of a hurry --- just before leaving to visit relations.

Paul

I would note that the largest known Cullen prime and Woodall prime were also found this past year. I also hope to find a new record prime of another well-known type in the next year (or at least write the software behind it). I won't metion what I'm looking for as there are too many competitive people who would try to beat me to it...

Does anyone know of new theorems or proofs from this past year for famous problems in the field of mathematics.

A front-page news item:

[url]http://news.yahoo.com/s/ap/20051227/ap_on_re_us/math_problem[/url]

Unfortunately, the name of the conjecture isn't even mentioned until the 7th paragraph! And strangely enough, the article is listed in the "Education" section...