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21h

comment 
The P VS NP problem as relates to factoring
Correction: The constant 2(2/3)^(2/3) in the preceding formula is valid (heuristically) only for integers of a special form. I think the best known constant for the general number field sieve is given in D. Coppersmith, "Modifications to the number field sieve," J. Cryptology 6 (1993), no. 3, 169180. This too is only heuristic. 
21h

comment 
The P VS NP problem as relates to factoring
@Adam P. Goucher: Incidentally, the expected running time exp( (2(2/3)^(2/3) + o(1)) (log n)^(1/3) (log(log n))^(2/3) ) of the number field sieve, is, to the best of my knowledge, heuristic and has not actually been proved. Also worth noting: the number field sieve is not a deterministic algorithm. 
Oct 28 
awarded  Good Answer 
Oct 15 
awarded  Nice Answer 
Sep 24 
awarded  Autobiographer 
Jul 15 
awarded  Nice Answer 
Jul 13 
answered  How does one justify funding for mathematics research? 
Jun 2 
awarded  Yearling 
Oct 19 
awarded  Necromancer 
Sep 13 
comment 
What is the expected number of random numbers (generated uniformly) such that their sum of numbers exceeds one?
This question was Problem A3 of the 1958 Putnam Competition (and as such is not researchlevel mathematics). 
Sep 13 
awarded  Informed 
Aug 20 
answered  Proof a Weyl Algebra isn't isomorphic to a matrix ring over a division ring 
Jul 29 
answered  Subgroups of finite index of fields 
Jun 25 
awarded  Revival 
Jun 2 
awarded  Yearling 
Jul 6 
comment 
How do you present a nonexistence theorem?
This story implicitly answers the problem of the student who shrugs upon hearing the theorem on bounded entire functions. By the time it occurs in a class it's very natural, but presented with it cold, the reaction of any student of normal inquisitiveness would be astonishment and an attempt at a counterexample. A student who isn't excited about celebrated classical results is perhaps best advised to find a field of study more to his liking. Incidentally, a result that has allured many a student into mathematics is, so to speak, a nonexistence nontheorem: the continuum hypothesis. 
Jul 6 
comment 
How do you present a nonexistence theorem?
My first reaction on seeing the title of this question was to recall Rota's "Ten Lessons I Wish I Had Been Taught": completely erase the blackboard, begin writing in the upper left corner, .... 
Jun 17 
awarded  Nice Answer 
Jun 13 
answered  When is a topological group Hausdorff (separated)? 
Jun 2 
awarded  Yearling 