Undergraduates make a “prime” discovery


This is cool:

Westfield State College senior mathematics majors Jeffrey P. Vanasse and Michael E. Guenette, working under the direction of Mathematics Department faculty members Marcus Jaiclin and Julian F. Fleron, have made a significant new discovery in the mathematical field of number theory. They have discovered the first known example of a 3 by 3 by 3 generalized arithmetic progression (GAP).

Most easily thought of as a 3 by 3 by 3 cube (similar to a Rubik’s cube puzzle) made up of 27 primes, their discovery begins with 929 as its smallest prime ends with 27917 as its largest prime. The intervening 25 primes are constructed by adding combinations of the numbers 2904, 3150, and 7440 in an appropriately structured method.

“Such an object was known to exist and its approximate size had been loosely estimated,” Fleron said. “However, a blind search would require checking more cases than can be feasibly checked by all existing modern computers each running for the next million years. Instead, the group used knowledge of the structural relationships between the potential candidates to greatly reduce the potential candidates to be checked.”

Whole thing here. It goes to show that students and faculty can work together to produce some really first-rate mathematics, if they’re put in a position to have the time and materials to make it happen and in an environment that really values that kind of scholarship. It also shows just how great of a role computing, especially computer programming, plays in doing mathematical research these days. Congrats to Jeffery, Michael, and their profs for a job well done.

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