SAT-wise, I was always better on the mathematical side of things than on the verbal, and I think the reason for that was that the abstractions made more sense to me than the literature I was studying at the same time: screw Mr. Darcy, Fermat’s got a theorem to prove!
Over the years, the poles migrated, or something, and now I write all the time and fumble for the calculator, but I can still relate to numbers or at least to some of them:
Prime numbers are those non-composite numbers that can only be divided by one or itself. On average, the gap that separates these numbers gets larger as their values increase. But a neat quirk about primes is that every once in awhile they also come in pairs, so-called twin primes. These numbers differ from another prime by two. Examples include 3 and 5, 17 and 19, 41 and 43, and even 2,003,663,613 × 2195,000−1 and 2,003,663,613 × 2195,000+1.
(Note: I did not check that last one.)
Ever since the time of Euclid, however, mathematicians have wondered if these twin primes keep on appearing for infinity. They have no doubt that primes themselves appear for infinity, but because mathematicians lack a useful formula to predict their occurrence, they have struggled to prove the twin prime conjecture the idea that there are infinitely many primes p such that p+2 is also prime (i.e. the two number gap).
We are, however, just a little closer:
The new result, from Yitang Zhang of the University of New Hampshire in Durham, finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on unproven conjectures. Although 70 million seems like a very large number, the existence of any finite bound, no matter how large, means that that the gaps between consecutive numbers don’t keep growing forever. The jump from 2 to 70 million is nothing compared with the jump from 70 million to infinity.
I am reasonably certain that I couldn’t make head or tail of Zhang’s research, but I did know that the largest known prime, as of this past January, consisted of 17 million digits, against which 70 million (which has only eight digits) is barely a rounding error. (If you care, it’s 257885161−1.)
Note: There are two houses on my block which bear prime numbers. Not twins, though.
(Via the Crimson Reach.)