Quote:
Originally Posted by davar55
Regarding your example, expanding the polynomial x^2 + x + 41.
Is there any way to PROOVE this is prime for
all integers x between 0 and 39 inclusive,
without actually testing or enumerating the range?

Good question, it was an olympiad problem in 1987, see:
http://www.artofproblemsolving.com/w...lems/Problem_6
So if we know that the above f(x)=x^2+x+41 is prime for f(0),f(1),f(2),f(3) then we know that it is also prime for f(4),..,f(39).
As I can remember there is a proof that there is only a finitely many such n value for that we can apply the statement, and we know all of them.