> Nicolau wrote :
> > 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.
>
>
> The computationally harder problem is to have f1(N) being primes of form 3n+1
> and f2(N) being primes of form 3n+2; f2 wins up to N=608981813029. For your f1
> and f3, f1(N)=f3(N) for N around 26932, around 615868, around 12311564 ...
>
> It's probably unwise to make large computational challenges on a list whose
> members almost by definition are interested in maths and have fast computers.
>
> Tom
Yes, I meant to state the harder problem, with 3n+1 x 3n+2, and mixed up things.
I am glad you corrected me.
The smallest counter-example the way I stated the problem is N = 26862.
What I do not understand is why you consider it unwise
to pose challenges to people who might actually be interested in them.
Maybe you consider "challenge" a bad word?
Or maybe you think I should have given a hint on how hard the problem is?
I did not mean to suggest that the members of this list
would or would not be capable to find the counter-example.
My point was that such a counter-example would large enough that:
(a) a na�ve person, seeing the empirical evidence,
would draw an incorrect conclusion.
(b) some members of this list might find it interesting to
consider the problem.
Nicolau
