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Tuesday, August 29, 2006

And i thought this was the PRIME of my life...

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.

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