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The Gabriela-star prime: a last and lasting gift

January 28th, 2011

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

Alfred Adler

“So what do acorporeals do, instead?”

Yann sat up and leaned against the side of the bed. “All the other things the embodied do. Give gifts. Show affection. Be attentive.”

“What kind of gifts?”

“Art. Music. Theorems.”

“Original theorems?”

“If you’re serious.”

Tchicaya was impressed. Mathematics was a vast territory, far more challenging and intricate than physical space. Reaching a theorem no one had proved before was a remarkable feat. “That’s positively… chivalric,” he said. “Like a knight riding off to the edge of the world, to bring back a dragon’s egg. And you’ve done that, yourself?”

“Yes.”

Greg Egan, Schild’s Ladder, chapter 8.

My arithmomania flaring the last few nights, I’ve been sleeplessly pursuing an elusive goal—one I frankly had no hope of achieving, yet one from which I couldn’t seem to pry myself. For reasons I can’t explain, even to myself, my most recent relationship has been punctuated by an urge to create. At times it’s been the usual Muse instinct of simply being inspired in some direction or other, but it’s also had manifestations of a blind urge: no particular inspiration, just the feeling that I ought to be making something. Often, I’ve been unable to help myself recalling the Current 93 lyric, “I wanted to write for you—songs, poems and bibles” for it’s very like the urge I felt, though I’m no poet or prophet (despite the name) and perhaps only rarely more than a mediocre musician. Still, there was the urge. And our time together did produce several pieces of music, from short, simple things, to some of my better recordings; some writing here and there, a few translations of my own; even some effort at returning my long out of practice hand to sketching, among other attempted acts of creation. But none have truly satisfied me; and I guess by this point, it’s obvious none satisfied her either.

I do not imagine this will fare better for either of us, but I felt myself again driven to produce something, and as it would be the last, I wanted to produce something lasting, something that could well outlive the both of us and any memory of us. Most of what I do, what I know how to do, is of fleeting interest and will scarcely outlive most times the time it takes to create it, much less wider swathes of time. But there is one field in which I sojourn from time to time that has a firmer bedrock, one that once chiseled tends to remain so, and so it is to that I turned.

It is no new theorem, alas, I have hewn out, but perhaps a unique thing nonetheless. From the infinite sea of prime numbers, I have fished out a heretofore unknown specimen with a number of distinct qualities I wanted to enshrine in it.

One of the first things to set it apart is the sheer size. While the number of primes is infinite, according to the database of largest known primes, only 5,383 known primes are larger than this 7,993-digit creature. On its own, 5,383 might seem a large number, but given the known primes tally in the millions, it’s a relatively tiny fraction.

There is a class of numbers known as the “star numbers“. They’re figurate numbers in the shape of a hexagram. The number of digits, 7,993, makes this a star number itself; specifically, the 37th—and 37 too is a star number—which number I chose as it will be my age this next October. While written out like a normal number, this looks like an odd jumble of random individual and runs of digits, if we write it out instead in the shape of the star, its mystery unfolds itself clearly.

Looking at it in that form—as you may do here, for the nonce, until I’ve time for a better presentation—you will see that the center is formed of the digits of the current year, 2011, radiating around to the points of the hexagram. Jumping out from there you find the numbers 1988, 3 and 11, which constitute the November birth date of my ex. In the context of primes, the date has a further significance in that it’s the anniversary of the 1961 first discovery of a titanic prime (in which group this prime also belongs). Continuing out, we find 22—her current age. At the edge, surrounding the whole figure, is the number 7. While it’s traditionally the number of Venus and signifies love, I chose it more particularly since the seventh letter of the Roman alphabet is “G”, her initial.

I will need at some point to draft a more formal, and better looking, web page to demonstrate the number than the one linked above; and once the formal primality proof certificate is completed, it will also turn up on the prime database’s Prime Curios page.

It may ultimately mean little, but it will definitely outlast me. Long after we’re forgotten, the number will remain, enshrining its little mystery, recalling somewhere how we were in this last year we had.

Mathematics is a dangerous profession; an appreciable proportion of us goes mad.

J. E. Littlewood

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Daniel Dockery's Portfolio

animî nostrî dêbent interdum âlûcinâri