How do you filter through published papers and find the ones you should read? Here's a paper that answered a long standing problem:
PRIMES is in P
so it would go at the top of the list for someone working in that area.
So, how do you find the most important results in some area for freely available publications or for ones requiring a paid subscription?
If there is no substitute for getting a paid subscription, then which online access subscriptions are the best?  
How can you even research and find what you're looking for with all of these barriers?
Thanks.
 A: One good way is to follow blogs written by and/or about individuals and/or communities that are related to your interest.
For example, I am very interested in finance research, Bayesian statistics, social signaling theory, behavioral economics, theoretical decision theory, and heuristics/biases/ratonality research. To a lesser extent, I am interested in complexity theory and quantum computing.
I follow Andrew Gelman's blog, Robin Hanson's blog, LessWrong, various topics at the arXiv, Scott Aaronson's blog, and a host of economist blogs.
Between all of these, there is usually a lot of discussion about classically important research articles, up-and-coming research programs and/or articles that are getting a lot of attention among experts, widely reported papers that have serious flaws, etc. I'm sure some good papers slip through the cracks here and there, but I've found it's a good way to keep current, to see what other expert-types have read or are currently reading, and to get lots of opinions about articles that I read. 
In particular, at community blogs like LessWrong, there is a 'discussion' area for informal posts. Since people there are also interested in Bayesian methods, I will sometimes post a short summary or interesting point about an article I have read. Sometimes no one else really reads my posts or responds, but other times it leads to a fruitful discussion with links to other good papers.
While maybe my answer is better suited for "keeping current," I definitely feel like keeping current is a good way to see which articles are referenced again and again, and which are perpetually recommended, especially by people you respect in a given field. Those are the papers to read up on. Also, look for places that keep track of citations. Papers with lots of citations are usually a good bet. Many times you can see the citations without buying the paper and then you can find it posted for free online.
Lastly, there are plenty of stack exchange communities for different branches of research. If you read a good paper or find an interesting problem type, usually you can post a question asking if anyone knows good papers in that field, and you'll get good responses.
A: You need access to Mathematical Reviews. Most established university libraries have a copy and that's what I would suggest for you. Online access is so expensive that it's not practical for an individual. MR has reviews of all published articles and these will help you filter out stuff you don't want to read. As far as access to the articles, many are still only available through subscription journals. However I sometimes find articles I'm looking for online. For those I often check the author's webpage first.
