ELLENSBURG, Wash. — Math students at Central Washington University say they’ve broken a 37-year-old world record for the largest weird number — a figure that stretches 226 digits long.
Weird numbers — yes, that’s actually a mathematically accepted term — are numbers that can be divided by smaller numbers that can never add up to the original number.
An example ... well, let’s hold off on that for a moment. Sufficient to say, mathematicians dating back to ancient Greece, maybe even earlier, have found these numbers both intriguing and difficult to discover.
And according to CWU math Professor Dominic Klyve, the 35-year-old who helmed the project, an increased knowledge of weird numbers leads to a better understanding of factorization, which is the basis of modern cryptography. Cryptography is the art of writing or solving codes, including encrpytion codes that are critical to secure Internet transactions.
A small group of undergraduate and graduate students in an honors seminar pulled off the breakthrough over the past two weeks.
As of Wednesday morning when CWU announced the news, the number had 127 digits. But by the afternoon it had grown significantly larger.
“We tried a lot of things that didn’t work and then a lot of things that did,” Klyve said.
The group has been using a cluster of 12 computer processors equipped with code written specifically for number theory.
What exactly is a weird number? Take 70, for example, which is the smallest weird number. It can be divided by 1, 2, 5, 7, 10, 14 and 35. No combination of those divisors can add up to 70. All weird numbers follow a similar pattern.
One of the students had brought up the topic of weird numbers weeks ago — an idea that caught Klyve’s attention. The concept of working with weird numbers was “doable,” he said, and concluded they would attempt the project. Over the two weeks, they would fail numerous times before succeeding, he said.
Previous record holder Sidney Kravitz had held the top spot since 1976, when he discovered a 53-digit weird number. Kravitz is the author of a mathematic formula written specifically for identifying the figures.
However, the group of five students surpassed that high mark numerous times, first finding a number with 74 digits.
The group will continue to push their calculations further, Klyve said. They intend to work through Christmas break in an attempt to find even larger number. He expects to publish their findings so that other prominent mathematicians get a chance to weigh in.
“There’s lots of things we don’t know about weird numbers,” said Paul Pollack, an assistant math professor at the University of Georgia who does a lot of work with closely related research. He said it will be great to hear what Klyve’s group has uncovered about the numbers, which he said have fascinated mathematicians for thousands of years.
The 226-digit number is 26,963,672,211,957,831,828,322,834,071,143,299,817,754, 720,290,127,404,079,937,026,385,368,922,075,196,690,720,690,562,498,337,038,657,263, 353,255,952,256,005,850,803,053,091,152,216,128,172,198,270,512,414,580,092,743,322, 379,544,478,286,025,897,899,890,351,444,085,611,625,835,160,270,418,964,124,507,243, 890,975,821,522,176,465,361,680,177,670,297,930,314,037,850,339,675,559,057,554,452, 347,547,946,165,134,639,879,111,112,583,151,946,671,967,876,920,506,598,818,088,728, 910,330,021,016,856,674,391,763,268,224,262,067,132,913,691,721,407,174,127,885,521, 288,146,239,271,038,154,486,086,650,600,357,888.