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A team of students has identified the first known example of a particular three-dimensional array of numbers that consists of 27 primes. Mathematics majors Jeffrey P. Vanasse and Michael E. Guenette, working under the direction of Marcus Jaiclin and Julian F. Fleron of Westfield State College in Massachusetts, made the discovery. The discovery is a 3-by-3-by-3 generalized arithmetic progression consisting of only prime numbers. An arithmetic progression is a sequence of numbers such that the difference between successive terms is a constant. A generalized (or multidimensional) arithmetic progression (GAP) allows for several possible differences.

The newly discovered array consists of 27 primes, with 929 as its smallest prime and 27917 as its largest. The 25 intervening primes are constructed by adding combinations of the numbers 2904, 3150 and 7440 in an appropriately structured way. The team was inspired by the work of Terence Tao of the University of California, Los Angeles and Andrew Granville of the Universite' de Montreal. Granville had written about generalized arithmetic progressions of primes in his article "Prime Number Patterns," which was published in the April issue of The American Mathematical Monthly. "We have been unable to find a 3-by-3-by-3 GAP of distinct primes," Granville had noted in his article.

MAA, Students Uncover a Novel Prime Progression, November 25, 2008.

Andrew Granville, Prime Number Patterns, American Mathematical Monthly, April 2008.

Cf. A113830, A113831.

Sequence in context: A072016 A061663 A054828 this_sequence A157183 A054829 A157935

Adjacent sequences: A153409 A153410 A153411 this_sequence A153413 A153414 A153415

bref,fini,full,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 25 2008