bounded primes? No, I mean, “bound gaps“. RTFA
I sent the link to the article on Yitang Zhang to Steve and Eric Cohen; I also posted elsewhere: Steve and Eric Cohen, the twinned sons of Paul J. Cohen, are making a film on the continuum hypothesis.
The Pursuit of Beauty
Yitang Zhang solves a pure-math mystery.
BY ALEC WILKINSON
Wilkinson’s article references “Prime Curios!” by BLANK to list 28 types of primes:
An obvious difference between Zhang in 2013 and Cohen exactly 50 years prior is that Paul had to write to Godel to know how right he was.
This is from graph 37 of the article, in a recent The New Yorker:
Prime numbers have so many novel qualities, and are so enigmatic, that mathematicians have grown fetishistic about them. Twin primes are two apart. Cousin primes are four apart, sexy primes are six apart, and neighbor primes are adjacent at some greater remove. From “Prime Curios!,” by Chris Caldwell and G. L. Honaker, Jr., I know that an absolute prime is prime regardless of how its digits are arranged: 199; 919; 991. A beastly prime has 666 in the center. The number 700666007 is a beastly palindromic prime, since it reads the same forward and backward. A circular prime is prime through all its cycles or formulations: 1193, 1931, 9311, 3119. There are Cuban primes, Cullen primes, and curved-digit primes, which have only curved numerals—0, 6, 8, and 9. A prime from which you can remove numbers and still have a prime is a deletable prime, such as 1987. An emirp is prime even when you reverse it: 389, 983. Gigantic primes have more than ten thousand digits, and holey primes have only digits with holes (0, 4, 6, 8, and 9). There are Mersenne primes; minimal primes; naughty primes, which are made mostly from zeros (naughts); ordinary primes; Pierpont primes; plateau primes, which have the same interior numbers and smaller numbers on the ends, such as 1777771; snowball primes, which are prime even if you haven’t finished writing all the digits, like 73939133; Titanic primes; Wagstaff primes; Wall-Sun-Sun primes; Wolstenholme primes; Woodall primes; and Yarborough primes, which have neither a 0 nor a 1.
Or broken down alphabetically:
emirp (wow! or hsog!)
neighbor (and naughty neighbor makes me think of the physics professor in the Coen Brothers’ movie)
(from 2009 — is that a prime? 2,009?)
see also: Aaron-Ruth (I mean Ruth-Aaron Pair of integers, by Carl Pomerance who I once tried to book, as a speaker into a Chicago pub)^please not that although Ruth-Aaron Pair does reference baseball, Cuban primes refers to cubes as in x^3 and not Orestes Minnie Minoso
see also: Sieve of Eratosthenes, by Mark Di Suvero
see also, or solve if you are bold: Riemann — and somebody needs to come up with a mnemonic device to remember i before e and two not one n’s. Riemann’s Hypothesis: can it be explained in 20 words? Check that: The Riemann Hypothesis, he was born in 1859, part of Hilbert #8, and simply put something about the distribution of primes way out on the number line, about the zeta function or landscape. Wiki.
What about 1,859?
What about the I-J-K-L gap? Why are the apparently, no types of primes whose name starts with those four letters? Or “I just killed Larry!?” I challenge mathematicians to discover new types of primes that refute that conjecture! I don’t have millions to offer as a prize, but I will buy you the coffee drink of your choice here at Coupa Cafe in Palo Alto, near Stanford.
And by the way, Vijay Iyer, the math-savvy jazz pianist, is reviewed favorably in the Times, by Ben Ratliff; it says his third cd as a leader of this trio is his best yet.
and1: talk about unclear on the concept, this from Stanford’s pr department, circa 2000:
Fabricated in 1999, The Sieve of Eratosthenes is typical of di Suvero’s sculptures in providing multiple readings and viewpoints as the spectator walks around it. The title reflects di Suvero’s interest in philosophy and humanistic concerns. It is named in honor of the Greek philosopher, geographer, and mathematician Eratosthenes (c. 275-194 B.C.), among whose achievements was the calculation of the circumference of the earth.
alter that day: New York Times reporting on this, about a year ago, Kenneth Chang, quotes Peter Sarnak (who is also an advisor to the Cohen Estate, and studied with Paul J. Cohen): if Twin Primes are consecutive odd numbers that happen to be prime, and the Twin Primes Conjecture, difficult to prove is an infinite supply of them, Zhang, thanks to work as close to me as San Jose State Goldston, took a boundary of 70,000,000 large but surely finite and like a large ruler passing along the number line, somehow proved that it works. Others using super-computers narrowed the gap or size or ruler or bound to 246, not quite “twins” as in 2, but closer. And yes, Zhang according to Wilkinson used a version of The Sieve of Eratosthenes so my wild association was not so silly. Meanwhile I still recall, and tell this endlessly (!) that the day the Times had a big spread on Gruska or whoever and Poincare — with a big drawing of a rabbit — I happened to sit down next to Paul at the computer time-share at the Old Main Library here, or he me actually, and mention this event, the article, and he dismissed it: “Only five people in the world now what they are talking about” but in fact I noticed that the same article was pinned to a board at his department. I don’t know if Steve and Eric have discussed their film with Peter Sarnak but it might be interesting to get him to compare the two events.
I just killed “I just killed larry”: contrary to as reported in Plastic Alto yesterday there is no intriguing gap between holy primes and mersenne. Primes in an alphabetical listing of types of primes like in Caldwell. For instance: invertible primes, like 109 and its invert 601. Iiptts!
edit to add, months later: Terry read this article and got excited, and texted it to Eric and Steve. So I re-read it, and also re-read this hot mess. The Simons Foundation also had a good story on it; an excerpt:
But that’s just on average. Primes are often much closer together than the average predicts, or much farther apart. In particular, “twin” primes often crop up — pairs such as 3 and 5, or 11 and 13, that differ by only 2. And while such pairs get rarer among larger numbers, twin primes never seem to disappear completely (the largest pair discovered so far is 3,756,801,695,685 x 2666,669 – 1 and 3,756,801,695,685 x 2666,669 + 1). (from May, 2013 as in more than a year ahead of the New Yorker version — is there a Hollywood version forthcoming?)