Nicolau C. Saldanha writes:
> > Given N, let f1(N) be the number of primes of the form 4n+1 which
> > are smaller than N, and f3(N) be the number of primes of the form
> > 4n+3 which are smaller than N. Thus, f1(10) = 1 and f3(10) = 2.
> > Is it true that f1(N) <= f3(N) for all N?
> >
> >The answer is no, but I challenge you to find a counter-example.
What I do not understand is why you consider it unwise to pose
challenges to people who might actually be interested in them.
"Challenge" in this context in English (at least as used in America)
often implies that you believe that it cannot be done or that it would
be very hard to do. It might be used to challenge someone to prove
Goldbach's Conjecture or Fermat's Last Theorem, for example.
Maybe you consider "challenge" a bad word?
Not a bad word, but it does sound like a difference in usage.
My point was that such a counter-example would large enough that:
(a) a naive person, seeing the empirical evidence,
would draw an incorrect conclusion.
(b) some members of this list might find it interesting to
consider the problem.
"Interesting", "difficult", and "non-trivial" would have been closer
to your intended meaning, then, I think. And if you simply wanted
someone to find a counter-example, just asking for one is fine; the
list has seen several conjectures proven and disproven (including at
least one of mine, on my Mersenne web page) by example.
Will
http://www.garlic.com/~wedgingt/mersenne.html
