Problems & Puzzles: Puzzles

Puzzle 366. Three questions about the PGP Patrick Capelle poses the following 3 questions about Prime-generating Polynomials, after the publication of the Final Report by J. C. Meyrignac, of the Al Zimmermann's Contest about the same subject, recently finished: Questions. 1.  Can you propose a polynomial of degree n (without absolute value), with integer coefficients, giving distinct and positive primes for all x, 0 <= x <= k(n)  and  k(n) > 37 + n ?   2.  Can you propose a cubic polynomial (without absolute value), with integer coefficients, giving distinct and positive primes for all x,  0 <= x <= 40  ?   3.  Can you propose a polynomial of the form x^n + x^(n -1) + ... + x + p, with p prime, giving distinct and positive primes for all x, 0 <= x <= k  and  k > 39 ?

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