Twin Prime Proof Erroneous

mindriot writes "The fairly recent perceived breakthrough in prime number theory regarding twin primes, as mentioned on slashdot, is apparently not quite perfect: 'On April 23rd, Andrew Granville of the Universite de Montreal and K. Soundararajan of the University of Michigan found a technical difficulty buried in one of the arguments in the preprint of Goldston and Yildrim. The main issue is that some quantities which were believed to be small error terms are actually the same order of magnitude as the main term. For now this difficulty remains unresolved.' A more detailed technical description is also available."

Comments

Re:A serious question - i'm not trolling, honest!

[HeghmoH]

Pi accurate to about forty-some digits would be accurate enough to calculate the circumference of a circle the size of the visible universe with an error the size of a proton.

How, exactly, is calculating billions of digits of pi useful, again?

On the other hand, primes are used for all kinds of good stuff, such as protecting your credit card numbers from evil people. Your conceptions seem backwards.

They could still pull it out

[drdale]

Remember that an error was found when the British mathematician first announced that he had a proof of Fermat's Theorem a few years ago. He was able to fix it, however, and AFAIK his proof is currently considered sound (albeit LONG).

Re:A serious question - i'm not trolling, honest!

[phliar]

I can understand calculating pi to the nth point as it is used in calculations...

That is not a very good reason! Let's say we use pi = 355/113 -- an approximation that's been known for many centuries -- to calculate the circumference of the earth. Using that value of pi our estimate will be off by about 30 feet (about 0.00003%). Even 22/7 is only off by 0.1%.

No; we calculate the umpty-bazillionth digit of pi for the same reason Mallory wanted to climb Everest: because it's there -- and there's cool shit to see along the way.