This afternoon, Yitang Zhang of the University of New Hampshire gave a special seminar at Harvard, in which he announced that he had proved that there are infinitely many pairs of prime numbers separated by no more than 70,000,000, a result differing only by a constant factor from the venerable twin prime conjecture. Dan Goldston, who together with Yildirim and Pintz made the last major advance on prime gaps, said, ""I was doubtful I would ever live to see this result." Not enough excitement for one day? Harald Helfgott has just posted to the arXiv a proof of the ternary Goldbach conjecture: every odd number is the sum of three primes.
posted by escabeche on May 13, 2013 - 51 comments

"Each prime number is represented by a bright, white square, whereas a non-prime ("composite") is grey. Visitors can select difference spatial arrangements of these numbers, ranging from several variants of the well-known Ulam Spiral, over the Archimedian spiral, to the more sophisticated 3D Hilbert curves." [more inside]
posted by jquinby on Apr 22, 2013 - 28 comments

What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."
posted by escabeche on Sep 18, 2012 - 61 comments

The Prime Game is not really much of a game, but it is a neat & little-known fact about the decimal representation of prime numbers.
posted by Wolfdog on Jul 10, 2007 - 24 comments

The math geeks have done it again. Yet another prime number which, when converted to binary, contains DeCSS: this one's an x86 Linux ELF executable. Only took a weekend of hacking to do, and it's only 752 bytes! You know what they say: when prime numbers are outlawed, only outlaws will have prime numbers.
posted by darukaru on Sep 11, 2001 - 0 comments

Mersenne Prime Search is a distributed computing project much like Seti@home, except instead of searching for aliens, you're in the running for $100,000 and a place in math history (shouldn't your computer actually be the one that goes into the math history books?).
posted by mathowie on Jul 7, 2000 - 1 comment