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Mathematicians Team Up To Close the Prime Gap
Hugh Pickens DOT Com writes "On May 13, an obscure mathematician garnered worldwide attention and accolades from the mathematics community for settling a long-standing open question about prime numbers. Yitang Zhang showed that even though primes get increasingly rare as you go further out along the number line, you will never stop finding pairs of primes separated by at most 70 million. His finding was the first time anyone had managed to put a finite bound on the gaps between prime numbers, representing a major leap toward proving the centuries-old twin primes conjecture, which posits that there are infinitely many pairs of primes separated by only two (such as 11 and 13). Now Erica Klarreich reports at Quanta Magazine that other mathematicians quickly realized that it should be possible to push this separation bound quite a bit lower. By the end of May, mathematicians had uncovered simple tweaks to Zhang's argument that brought the bound below 60 million. Then Terence Tao, a winner of the Fields Medal, mathematics' highest honor, created a 'Polymath project,' an open, online collaboration to improve the bound that attracted dozens of participants. By July 27, the team had succeeded in reducing the proven bound on prime gaps from 70 million to 4,680. Now James Maynard has upped the ante by presenting an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower. Zhang's work and, to a lesser degree, Maynard's fits the archetype of the solitary mathematical genius, working for years in the proverbial garret until he is ready to dazzle the world with a great discovery. The Polymath project couldn't be more different — fast and furious, massively collaborative, fueled by the instant gratification of setting a new world record. 'It's important to have people who are willing to work in isolation and buck the conventional wisdom,' says Tao. Polymath, by contrast, is 'entirely groupthink.' Not every math problem would lend itself to such collaboration, but this one did."
We cannot allow a prime gap!
If they keep this shit up, pretty soon they will prove that every number is prime.
>> which posits that there are infinitely many pairs of primes separated by only two (such as 11 and 13)
Yawn. Call me when you find a set of primes separated by one.
Three people are asked to prove that all of the odd numbers are prime - a physicist, a mathematician and a programmer.
The physicist goes first. "3 is a prime, 5 is a prime, 7 is a prime, 9 is a ... oops, experimental error, 11 is a prime ...".
Next the mathematician takes a crack at it: "3 is a prime, 5 is a prime, 7 is a prime, and the rest by induction".
Finally it's the programmer's turn. "3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime ...".
What do I win?
The tattered remnants of Anne_Nonymous's (probably not her real name) Geek Card, in a frame.
Wow. That's like so deep man.
I call BS. That gap is only N-2.
Does anyone happen to know what the greatest known lower bound is? (i.e. the largest known difference of two successive primes?)
There is none.
Proof: Select an arbitrarily large number N. The numbers between (N! + 2) and (N! + N) are all composite ((N! +2) is divisible by 2, (N! + 3) is divisible by 3, ..., and (N! + N) is divisible by N). Since you can find an arbitrarily large span of composite numbers, there is no upper bound on the gaps between primes.
QED.
Wrong set. You're dealing with ALL primes. The question is about the set of KNOWN primes (you know, the ones listed in the NSA's Big Book of Primes). Between the known primes, there is a greatest known lower bound.
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