Twin Prime Proof Proffered

HateBreeder writes "Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many Prime Twins, it seems that a hole has recently been found in the proof, however mathematicians remain hopeful that the proof can be corrected."

Comments

twin primes.

[rubberbando]

Before I go into my spiel, I will admit that I am no scientist or mathematician.

I always have had an obsession with the pattern of prime numbers. Now and then I get motivated and download a current list of those discovered. With that I try to find some magical pattern, in hopes of finding a secret message or formula explaining reality. When that announcement was made in the previous slashdot story, I did find the claim of infinite primes to be troubling. From my own observations, I believe the gaps between primes may fluctuate greatly but the maximum and minimums grow ever higher. To me these gaps look like some sort of waveform. If I had better coding skills in the manipulation of sound, I would write a program to generate a sound wave out of these numbers. Does anyone know if this has been tried and if so, what was discovered?

Re:twin primes.

[Lifewish]

Good summary from a waveform perspective.
There are definitely an infinitely large number of primes. Proof: assume a finite number of primes p1,p2,...,pn (counting from smallest to largest). Then p1*p2*...*pn + 1 is divisible by none of these (hence is prime) and is larger than pn. This is a contradiction of the original assumption, which must therefore be wrong. Hence there are an infinite number of primes.

Re:twin primes.

[Kjella]

First, I assume you mean twin primes. Proving infinite primes is trivial and from ancient Greece. It is a proved fact that there are arbitrarily large gaps in the prime sequence (i.e. infinitely large gaps). And that primes get rarer and rarer, in the limit, infinitely rare. Neither of those means that the number of primes is finite.

Basicly, if you set it up as a probability statement:
p( prime ) -> 0
p( prime pair ) -> 0

The latter will simply go towards 0 a lot faster than the former. All you would need to prove is that there must be one more pair (which is not trivial) and you're done.

Take the greek proof, where you multiply all known primes and add 1. Imagine if you took say, the 1000 smallest primes. All it proves is that there's a prime q <= p1*p2*....*p999*p1000+1. That product will be much much greater than any one of the primes. All it takes it one in the entire interval, and the total is infinite.

Kjella

Re:twin primes.

[locofungus]

It's trivial to prove that there is an arbitrarily long sequence of numbers with no primes in it.

(n+1)!+2 ... (n+1)!+n+1 is a run of n numbers none of which are prime.

Of course, this doesn't mean that you have to go all the way to (n+1)! before you can find a run of n numbers without a prime, merely that such a run must exist.

Way to keep on top of things!

[HiLander4237]

News that's only 5 months out-of-date.

Re:old news

[gnalle]

A simple Google search reveals that the story is a dupe. Search the old threads for cool comments to boost your karma :)

When I get more time I want to make a perl script that wgets slashdot.org once an hour and searches google for dupes. It is probably enough to test if any links from present slashdot stories have appeared on the site before, but perhaps I can find a way to pick out relevant title words. Once my script has found a dupe it should pick a few highrated comments from the old thread and repost them :)

Re:Withdrawn

[gartogg]

I understand that it's flawed, but Is there any place the original (flawed in lemma 8) proof can be viewed?

(I went to GA Tech for a semester...)

Re:I like a good alliteration as much as anyone

[reverseengineer]

It was proffered a long time ago. The news is that it doesn't work. May I suggest punctured?

A couple years ago, there was a proposed proof to the Poincare conjecture- not the Perelman proof which AFAIK still holds together, but another attempt which was soon found to have an insurmountable problem. When the proof was first announced, the Mathworld news item ran, Poincaré Conjecture Purportedly Proved, and when the hole in the proof (essentially, an unproven step used in the proof) came to light, the headline was Poincaré Conjecture Purported Proof Perforated.