Abundant Weirdness: Our Journey to Breaking a World Record

In Fall 2013, the Math Honors Seminar at Central Washington University broke the world record for largest primitive weird number ever discovered. A weird number is a number N whose set of proper divisors sums to be larger than itself, but which has no subset of proper divisors exactly equal to N. Take, for example, the number 70, which has proper divisors {1, 2, 5, 7, 10, 14, 35}. The sum of these numbers is 74, a number that is larger than our original number. Though, this only satisfies one of the qualifications for the number 70 to be considered “weird.” In particular, 70 is a weird number because no subset sum of {1, 2, 5, 7, 10, 14, 35} equals 70. The most important class of weird numbers is the primitive weird numbers – those not divisible by any others. Thousands of primitive weird numbers are known, but there is no efficient way to find them all. By early 2013, the record for the largest known primitive number was held by Dr. Sidney Kravitz, who discovered a 53-digit weird number. Using a generalization of Kravitz’s ideas, the class broke this record, finding weird numbers with 74, 127, and 226 decimal digits