The TI-89 supports arbitrary-precision integers, which is pretty cool — who would’ve expected a little graphing calculator to do that? And the TI-89 also has an isPrime() function to run primality tests on bigints. (I’m guessing it does some trial factoring, followed by Fermat’s test.)
But isPrime() only works on integers up to 1,016 bits long. If you try it on a bigger number that has no small factors, it’ll throw an Overflow error (probably because it runs out of bits when squaring for Fermat’s test).
So 2^1016 + 15 is the smallest number that isPrime() overflows on. And it’s definitely not prime. But what are its factors???
Well, using a top secret technique, I’ve managed to factor 2^1016 + 15. So here for the very first time is its never-before-seen factorization!
2^1016 + 15
= 702223880805592151456759840151962786569522257399338504974336254522393264865238137237142489540654437582500444843247630303354647534431314931612685275935445798350655833690880801860555545317367555154113605281582053784524026102900245630757473088050106395169337932361665227499793929447186391815763110662594625551
= 30318252213686189666631745855022701189
× 547160149672958111942125251432194342119
× 42330848468747673729654918007133622045022643929194477276261348631874202201981045134332283399052704102669234594840943290240896044770301345078520599843003984098534102753493658463400599745849980683500043056536210696972783287620102661
Mwahahaha!
(Tomorrow I’m gonna factor 2^1277 − 1. It can’t be much harder, right?)
Copyright © 1998 David Chau. All rights reserved. [Home]