I'm not sure if it's been mentioned here. The latest Al Zimmermann Programming contest shattered all existing records in the field of Prime Generating Polynomials. For example, one polynomial that generates 49 primes is x^4 - 97*x^3 + 3294*x^2 - 45458*x + 213589, first found by Mark Beyleveld and later by 5 other participants. Even better polynomials were found. More results: CUBIC: -66 x^3 + 3845 x^2 - 60897 x + 251831. Prime for x=0 to 45. Ivan Kazmenko and Vadim Trofimov. 42 x^3 + 270 x^2 - 26436 x + 250703. Prime for x=0 to 39. Jaroslaw Wroblewski and Jean-Charles Meyrignac. QUARTIC: x^4 - 97x^3 + 3294x^2 - 45458x + 213589. Prime for x=0 to 49. Mark Beyleveld. QUINTIC: (x^5 - 133 x^4 + 6729 x^3 - 158379 x^2 + 1720294 x - 6823316)/4. x=0 to 56. Shyam Sunder Gupta. x^5 - 99x^4 + 3588x^3 - 56822x^2 + 348272x - 286397. x=0 to 46. Jaroslaw Wroblewski & Jean-Charles Meyrignac. SEXTIC: (x^6 - 126 x^5 + 6217 x^4 - 153066 x^3 + 1987786 x^2 - 13055316 x + 34747236)/36. Prime for x=0 to 54. Jaroslaw Wroblewski & Jean-Charles Meyrignac. Full details and findings will eventually be published at At http://www.mathpuzzle.com/ I have about 40 other math stories... it's been a busy month. Ed Pegg Jr