Gil: I am not so familiar with this aspect of complexity theory, so did not figure out how to write a proper remark about the implications of full derandomisation. I’ll put the remark on the wiki instead (which we already link to regarding the oracle counterexample showing that P=BPP is not sufficient).

]]>fast algorithm to locate primes. Unfortunately, to use the P = BPP conjecture, one

would presumably need to obtain a bounded-error probabilistic polynomial (BPP) time

algorithm for solving the above decision problem (or some closely related problem), and

it is not clear how to achieve this.”

Maybe we should mention in one sentence that the required result will follow from “Full derandomization” http://blog.computationalcomplexity.org/2006/07/full-derandomization.html which itself follows from some very harsh hardness result. Then there was a comment (but I forgot where) by Avi Wigderson that full derandomization is much more than needed because of some unary nature of the problem which implies that less harsh hardness result (for turing machines rather than circuits) would suffice.

]]>https://svnbackup.xp-dev.com/svn/Finding_primes/

and specifically

https://svnbackup.xp-dev.com/svn/Finding_primes/polymath.pdf

for the most recent version. (I also placed it on my blog at

http://terrytao.files.wordpress.com/2011/02/polymath.pdf

in case the other link does not work well.) I’ve now implemented all the referee changes; I’ll wait for a few days to see if the other contributors have something to say and then will send back the revision.

]]>