Prime Generating Polynomial Records
The latest "Al Zimmermann Programming Contest" shattered all existing records in the field of Prime Generating Polynomials.
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. Six people found this record-setting polynomial within weeks of each other!
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.
Source: www.mathpuzzles.com
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