Mathematics students at Central Washington University have broken a world record—they found the largest “weird number” yet discovered: 1,304,478,802,221,037,336, 898,806,955,880,590,950,108,213,611,184,211,428,152,436, 309,358,286,058,099,789,749,839,735,498,620,012,494,920,476,023,972,998,095,015,247,872.
Mathematicians use the term “weird” informally to describe a number that has unusual characteristics. In this case, a weird number is one in which no combination of its divisors add up to the original number. Divisors are numbers that can be divided into a whole number to yield a quotient that is a whole number. For example, in the smallest weird number, 70, its divisors are 1, 2, 5, 7, 10, 14, and 35. No combination of these numbers will add up to 70. Weird!
According to Dominic Klyve, CWU mathematics professor and advisor, a better understanding of weird numbers leads to a better understanding of factorization, which is the basis of all modern cryptography—the art of writing or solving codes.
No one knows how common weird numbers are, and looking for big ones is hard. Until last week, the previous record had stood for more than 35 years—the reigning champion was a 53-digit number discovered by Stanley Kravitz in 1976. Then a group of five CWU students—Luke Campbell, Anna Cockrum, Jacob Darst, Jeremy Klarich, and Michael McDonald—together with Klyve, decided to try to find a bigger one.
Such a search requires both creative thinking and computing power. Bill Glessner of CWU’s Networks and Operations division of the Information Technology office set up several old research computer clusters for students and faculty. By working quickly during seminar, and holding early morning meetings to pursue their mathematics before classes started, the math team found a way to use Kravitz’s ideas from his 1976 paper to look for weird numbers on some of these computer clusters.
Their method quickly proved successful. They broke Kravitz’s record by finding a 74-digit weird number. Encouraged by their success, they pushed their calculations further—at last count, they had found over a dozen numbers which break the old record—the largest so far is 127 digits. They plan to keep working through Christmas break, and hope for several new world records in the near future.