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Post Info TOPIC: Twin prime conjecture


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Mersenne prime
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Mathematicians at UCLA have discovered a 13-million-digit prime number, a long-sought milestone that makes them eligible for a $100,000 prize.
The group found the 46th known Mersenne prime last month on a network of 75 computers running Windows XP. The number was verified by a different computer system running a different algorithm.

"We're delighted. Now we're looking for the next one, despite the odds" - UCLA's Edson Smith, the leader of the effort.

It's the eighth Mersenne prime discovered at UCLA.

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Ulam spiral
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The Ulam spiral, or prime spiral (in other languages also called the Ulam cloth) is a simple method of graphing the prime numbers that reveals a pattern which has never been fully explained. It was discovered by the mathematician Stanisaw Ulam in 1963, while doodling on scratch paper at a scientific meeting. Ulam, bored that day, wrote down a regular grid of numbers, starting with 1 at the centre, and spiralling out:

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Poincare conjecture
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A reclusive Russian won an academic prize Tuesday for work toward solving one of history's toughest math problems, the Poincare conjecture, but he refused to accept the award - a stunning renunciation of accolades from the top minds in his field.

Grigory Perelman, a 40-year-old native of St. Petersburg, was praised for work in the field known as topology, which studies shapes, and for a breakthrough that might help scientists figure out nothing less than the shape of the universe.
But besides shunning the medal, academic colleagues say he also seems uninterested in a separate, $1 million prize he might be awarded for his feat, which proved a theorem about the nature of multidimensional space that has stumped people for 100 years.
The Fields Medal was announced at the International Congress of Mathematicians, an event held every four years, this time in Madrid.
Three other mathematicians - another Russian, a Frenchman and an Australian - also won Fields honours this year. They received their awards from King Juan Carlos to loud applause from delegates to the conference. But Perelman was not present.

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A proof for the Poincare Conjecture will appear in an upcoming edition of the Asian Journal of Mathematics.
Two Chinese mathematicians, Zhu Xiping and Cao Huaidong, have put the final pieces together in the solution to the puzzle that has perplexed scientists around the globe for more than a century.
A Columbia professor Richard Hamilton and a Russian mathematician Grigori Perelman laid foundation for the latest endeavours made by the two Chinese. Prof. Hamilton completed the majority of the program and the geometrisation conjecture.

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Russian mathematician Grisha Perelman is on the verge of collecting $US1 million ($1.35 million) for solving the Poincare Conjecture. one of the seven greatest mathematical problems of all time, and was first posed by French mathematician Henri Poincare in 1904.

"The word is he's got it. But no one wants to say so in case they're wrong" - mathematician Thomas Hales of the University of Pittsburgh.

According to Professor Devlin, a mathematician at Stanford University in California, the conjecture proposes a way to tell if a bizarre-looking object is an ordinary three-dimensional object in disguise, and is about the "mathematics of smooth behaviour".

The Millennium Prizes were established in 2002 by the Clay Mathematics Institute in Cambridge, Massachusetts, as a challenge to mathematicians.
Four years ago, Perelman thought he had cracked the problem. But the Clay Mathematics Institute rejected his solution, or proof. It did not meet the institute's strict requirements: a peer-reviewed publication of the work, as well as a two-year waiting period to see if the solution stood up to scrutiny.
Professor Devlin, for one, predicts that the CMI is more likely to pay out for the solution of another millennium problem, the so-called Reimann Hypothesis.
It looks at how randomly prime numbers -- divisible only by themselves or 1 -- are sprinkled along a line of numbers. Together with three other millennium problems, the hypothesis is key to internet security.

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Twin prime conjecture
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Mathematicians have taken a giant step towards cracking one of the oldest and most complex number puzzles - without a Sudoku grid in sight.
The puzzle, known as the twin prime conjecture, has stumped the best mathematical brains for centuries.
Of similar status to Fermat's last theorem, it even appeared as the subject of a chat-up line in the 1996 Hollywood film The Mirror Has Two Faces.
Now, number experts Dan Goldston of San Jose State University in California and Cem Yildrim of Bogazici University in Istanbul, working with Janos Pintz of the Hungarian Academy of Sciences, have paved the way for a solution. Prof Goldston announced the breakthrough at the American Institute of Mathematics in Palo Alto, California.

"A couple of months ago I would have told anybody who asked that no one has ever had a plausible idea for proving the twin prime conjecture. Today, I think it is feasible that it will be resolved in the next few years." - Brian Conrey, director of the institute.

The twin prime conjecture proposes there are an infinite number of paired prime numbers that differ only by two, such as 3 and 5, 11 and 13, 29 and 31.
But as the size of the prime numbers soars, so does the difficulty of keeping track of them.
The trio's work does not prove that huge prime numbers also crop up in pairs, but it suggests they are likely to, based on an analysis of the average size of the gap between them.
In effect, they have paved the way for the full solution of the riddle.
"This is one of those problems that, if you can prove, you will write your name in mathematics history. A lot of these things are very simple to state, but incredibly difficult to prove." - Marcus du Sautoy, a mathematician at Oxford University


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