I know this site is for mathematical questions and answer places, but I need a little help from you in some other aspect. I have searched in google but didn't get any satisfactory answer for it. This is why I am requesting you to help me or atleast provide me some information or link from which I can get my answer. Also I apologize as I could not figure out what should be title and tags for this query so I gave some thing.
The query is: "fermat's primes are finite" ---is it still a conjecture? What are the researches have been made so far? In arxive I didn't get any such special thng. One more thing, is there any special prize money declared on this conjecture? If so, how can I know that?
Please provide me some details or any links where I can get the answers. I know it is not any mathematical problem to ask for help but I have tried to get the answer but in vain. Please help me.
Thanking you in advance.
Several individual mathematicians have proposed as rewards and/or incentives for the solution of various conjectures moderate or insignificant sums of money, and even rather exotic objects. The late Paul Erdős was (also) famous for the former, and Stanislaw Mazur awarding Per Enflo a live goose (see the details on the link) is an example of the latter.
In a rather different perspective, Andrew Beal (a banker) offers a hefty sum for the proof of a conjecture named either after him or Tijdeman-Zagier conjecture.
Apart these and the infamous Millenium prize problems (associated to vastly higher sums of money), the lists of such prizes that I know do not include the result you are interested in, hence the answer to your question is most probably: No.