# Prime Number Patterns

Award: Lester R. Ford

Year of Award: 2009

Publication Information: The American Mathematical Monthly, vol. 115, no. 4, April 2008, pp. 279–296.

Summary: In 2005, Green and Tao combined ideas from many parts of mathematics to prove that for any positive integer k there are infinitely many distinct pairs of non-zero integers (a,d) such that a+jd is prime for each integer j in {0, 1, …, k-1}. In this engaging paper, Granville considers conjectures he formulated to probe beyond a horizon made more remote by Green and Tao. To his surprise many of his conjectures followed fairly directly from the work of Green and Tao.

About the Author: (from the Prizes and Awards booklet, MathFest 2009) Andrew Granville is the Canadian Research Chair in number theory at the Université de Montréal. His awards include the Presidential Faculty Fellowship in Mathematics (from President Clinton) in 1994, the 2008 Chauvenet Prize of the MAA, and the 2006 Jeffery-Williams Prize of the Canadian Mathematical Society. He was an invited speaker at the ICM in Zurich in 1994, and a plenary speaker at the Joint Mathematics Meetings of 1996 and 2002. He was recently elected a Fellow of the Royal Society of Canada.

Author (old format):
Andrew Granville
Author(s):
Andrew Granville
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Publication Date:
Wednesday, September 2, 2009
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In 2005, Green and Tao combined ideas from many parts of mathematics to prove that for any positive integer $k$ there are infinitely many distinct pairs of non-zero integers $(a,d)$ such that $a+jd$ is prime for each integer $j$ in $\{0, 1, …, k-1\}$. In this engaging paper, Granville considers conjectures he formulated to probe beyond a horizon made more remote by Green and Tao. To his surprise many of his conjectures followed fairly directly from the work of Green and Tao.