if $P(x) = x^2 + x + 41$ compute for $x = 1,2,3..10$ and check if the values are prime. I have solved this by trial division. Might it be that P(1), P(2), P(3)... are all primes? This one is out of my depth. I vaguely suspect that proof by induction is the way to go but i do not know how. Please guide me through the proof or to relevant readings that will help me.
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1They are prime up to and including $x=39$. But not at $40$, nor at $41$. It is not known whether there are infinitely many primes of this shape. – André Nicolas Mar 23 '15 at 18:24
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1For reading, you could start with this. – André Nicolas Mar 23 '15 at 18:33
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You are welcome. Your computations were the sensible approach. – André Nicolas Mar 23 '15 at 19:43