A few days ago I did a bit of drive-by blogging to lodge a mild complaint against my occasional arithmomania. At the time, my goal was eluding me and the problem seemed altogether intractable, thus my irritation.
I have since, however, succeeded. (Yes, I know, it surprises me, too, but miracles happen sometimes!)
Pretending for a moment that Adler was incorrect in the earlier quotation, I will attempt briefly to explain what I've done. At the most basic, I've discovered a new prime; technically, a "titanic prime". Well, perhaps not "new", as surely the number existed in some abstract sense before any of us were aware of it, but it has never before been known in the literature or records, and it's a peculiar beast in its own right.
One of the things that makes it so is its sheer size: written out, the number is 7,993-digits long! While there is an infinity of primes, according to the database of largest known prime numbers, there are only 5,383 known prime numbers larger than this; and while 5,383 might seem a large amount, considering there are millions of known primes, it's a relatively tiny fraction.
Adding to the oddments, this is a star-congruent prime. What that means is that if you write the digits out in the positions and shape of the 37th star number (with the index, 37, itself being a star number, and chosen as, unfortunately, it will be my age next October), the seemingly random jumble of digits comprising this number reveal obvious, unmistakable patterns.
Specifically, it will be seen that the number takes on the shape of a hexagram (for Siouxsie and JJ), and spiraling around the center is the number 2011, the current year. If you go out from there, you'll find 1988, then 3, then 11—the date, 11-3-1988. While already a meaningful date, in terms of primes it has even another meaning in that November 3rd is the anniversary of the discovery of the first titanic prime in 1961. Moving farther out, we find the number 22, the current age in 2011 of someone born on that 11-3-1988 date. And going to the outermost edge of the figure, we find the whole surrounded by the number 7—chosen as the seventh letter of the alphabet is "G", an initial. The rest of the star is filled with zeroes.
The figure is too large to demonstrate within the constraints of blogger, but as seeing it makes it far more understandable than reading about it, I have a temporary presentation available here. I will flesh out the page later into something more presentable and move it to a more public URL, as Dr. Pickover has already asked about publishing and linking to it. Once the formal primality proof certificate is completed, it will also turn up on the prime number database's Prime Curios page.
"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.
Sorry, yes, I'm a "bit" of a geek.
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