Archive for September, 2008|Monthly archive page
Some really big prime number just got found
Mathematicians at UCLA have just discovered a prime number with almost 13 million digits. Prime numbers, of course, are only divisible by themselves and one; it has been known since Euclid in the third century BCE that there are an infinite number of prime numbers.
However, this is a special type of prime number called a Mersenne Prime. Named for 17th century French mathematician Marin Mersenne, these numbers are simply one less than a power of two (2^n – 1). Only 47 have been discovered to date, all but ten of them first identified since the start of the 20th century. Incidentally, the largest currently known prime number happens to be a Mersenne Prime: 243,112,609 − 1.
Math people get really excited over these numbers and when new ones are discovered. I don’t see why. There is no practical use for these numbers. What’s the big deal? I could just as easily make up the “Jacob Prime” which, uh, is… three four less than a power of two. Wow; how special is that? Yeah, okay, it sucks—but that’s my point.
But I don’t dislike prime numbers. One thing about them that I do find very interesting is the Ulam spiral phenomenon, named after its discoverer, Polish mathematicial Stanislaw Ulam. He stumbled upon them while at doodling at a really boring meeting (probably where they were discussing Mersenne Primes) and you can produce the phenomenon this way: (1) write down all integers starting at one point and spiraling outward (see firgure 1 below) and then (2) either circling, as Ulam did, all the primes, or, as below, removing all the non primes (see figure 2).

Start by writing all integers in a spiral, then remove all the numbers that aren't prime to find something quite interesting...
Once you have done enough numbers—and it doesn’t take many—you’ll see that the prime numbers tend to occur along orthogonal lines. See, for instance, the lines formed by 3-13-31, 41-19-5, and 19-7-23-47 in figure 2.

The Ulam spiral phenomenon is clearly seen here on a 200 x 200 grid. Note the diagonal lines throughout the image.
All prime numbers, except for 2, are odd numbers; and since in the Ulam spiral adjacent diagonals are alternatively odd and even numbers, it is not surprising that all prime numbers lie in alternate diagonals. However, what is surprising is the tendency of prime numbers to lie on some diagonals more than others; there is no apparent reason for this to be. This tendency occurs on any scale and regardless of what integer you start with at the middle. At right is a 200 x 200 grid of numbers and the effect is clearly seen. I am furthermore told that, at sufficient distances from the center, horizontal and vertical lines also become evident.
This effect is built into the nature of numbers, it’s not something that some guy just made up. Admittedly, it’s no more useful than Mersenne primes, but it’s a whole lot cooler and doesn’t take huge amounts of computing power to play around with—just grab a piece of paper and a pen!
Anyway, those guys who found the 13 million digit Mersenne prime are going to win $100,000 (I told you, mathematicians go nuts over these things). I’ll give a nickel to whoever finds the first Jacob prime with more than 1207 digits. Start your calculators!
China performs space walk, rips off Star Trek
Congratulations to the People’s Republic of China, which has launched their third crewed mission to space and Zhai Zhigang, age 41, has successfully performed his nation’s first space walk. The spacecraft, the Shenzhou 7, has a crew of three astronauts—or taikonauts, as the Chinese call them (cf. cosmonaut). Besides China, only the United States and the Soviet Union/Russia have launched people into space.
China hopes to establish a space station by 2020 and also has plans to land people on the Moon and, eventually, Mars. They made the news last year when they shot down an old satellite in a test of their military abilities; this was largely seen as a provocative act and a possible threat to the United States, which maintains considerable assets in space for both communication, intelligence, and scientific purposes.
I am also struck, however, by the unoriginality of the China National Space Administration logo. Just look at it. Doesn’t it remind you of something? If you’re a fan of Star Trek, I’ll bet that it does. Compare:
Regardless of where the logo came from, Godspeed to the three taikonauts, Zhai Zhigang, Liu Boming, and Jing Haipeng.
Something outside observable universe pulling galaxies
Cosmologists have discovered that 700 clusters of galaxies are being pulled by a massive gravity source that is outside the observable universe.
Since the universe is approximately 13.7 billion years old we can see no more than about 13.7 billion light years in any direction. However, the entirety of the universe is larger—potentially unimaginably larger—than that due to an early expansionary phase in the universe in which space itself expanded at an incredible rate. The mass that is pulling on those galaxy clusters, each of which is made up of many galaxies, lies beyond our event horizon, outside the observable universe.
Some of the researchers hypothesize that the mega mass in question is the result of an area of the universe that did not undergo as extensive a period of hyper inflation, leading to a more dense area of space.
In these regions, space-time might be very different, and likely doesn’t contain stars and galaxies (which only formed because of the particular density pattern of mass in our bubble).
It could include giant, massive structures much larger than anything in our own observable universe. These structures are what researchers suspect are tugging on the galaxy clusters, causing the dark flow.
“The structures responsible for this motion have been pushed so far away by inflation, I would guesstimate they may be hundreds of billions of light years away, that we cannot see even with the deepest telescopes because the light emitted there could not have reached us in the age of the universe,” Kashlinsky said in a telephone interview. “Most likely to create such a coherent flow they would have to be some very strange structures, maybe some warped space time. But this is just pure speculation.”
Needless to say, scientists are very surprised at this unexpected finding.
Palin protected from the probing presence of the press

She can give a speech, but if this woman can't take questions from the American press corps, do we really want her meeting with hostile foreign leaders when it counts?
Alaska governor and Republican vice presidential nominee Sarah Palin visited with foreign heads of state yesterday and today, including Afghan President Hamid Karzai, Colombian President Alvaro Uribe, and Pakistan’s newly elected President Asif Ali Zardari. Palin has accumulated little to no foreign policy experience so far in her political career and didn’t travel outside of North America until last year. This is her first opportunity to meet with foreign leaders.
The meetings are designed in part as a photo op, to show her meeting world leaders and thus enhance her foreign policy credentials in the eyes of voters. It is also to continue her crash course in foreign affairs ahead of the upcoming Vice Presidential debate with Senator Joe Biden, the chairman of the Senate Foreign Relations Committee. To this end she also met with former National Security Advisor and Secretary of State Henry Kissenger.
The meetings have all been tightly choreographed and carefully controlled. Palin has taken no questions from the media. Initially, John McCain’s campaign wanted to exclude reporters even from the photo ops, in case they might overhear something worth reporting or maybe ask a question. However, the five major TV networks threatened to boycott the meetings and not broadcast the pictures and video if no reporter could be present. The McCain campaign relented; a journalist was allowed to be there, but not to ask any questions.
Today, the foreign policy crash course continued with Palin and McCain scheduled to meet with the Presidents of Urkarine and Georgia, Viktor Yushchenko and Mikheil Saakashvili, respectively. They were also to speak with U2 singer Bono and Indian Prime Minister Manmohan Singh. Previously, Palin had cited Alaska’s proximity to Russia as evidence of her international exposure and her foreign travel has been so scant that her campaign initially counted a touchdown in Ireland as a visit. She has backed away from both claims.
Today, First Lady Laura Bush, while openly acknowledging Palin’s lack of foreign policy experience, characterized her as a “quick study.” We’d better hope so.
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