Official Odd Perfect Number thread - Page 2

patdumpsite · 2006-12-15, 13:02

Has the OPN conjecture been settled?

I came across the following:

http://arxiv.org/PS_cache/hep-th/pdf/0401/0401052.pdf

This paper claims to have settled the nonexistence in 2004, was there a problem found within this publication?

I have read nothing about it anywhere but in this paper, but if this was published two years ago, I would have thought that most people would have heard about it by now, which is why I am asking if there was a problem.

I am just curous if anyone knows what's going on.

patdumpsite · 2006-12-18, 14:33

I did more searching and I came across this thread at sci.math.

So I guess people do not seem to believe the proof is correct.

Pascal Ochem · 2008-10-23, 12:11

wblipp cites an old paper (1957) for the result that the largest exponent in an OPN is at least 4.
http://oddperfect.org/against.html
Has this been improved ?
I cannot prove that the largest exponent is at least 5,
but I can obtain something like "an OPN containing no exponent strictly
greater than 4 must be greater than 10^10000".

Zeta-Flux · 2008-10-23, 13:43

Pascal,

There was a recent paper that, using sieve techniques, proved that for any given finite set of exponents, there is an upper bound for the first OPN having exponents only in that set (I think even ignoring the exponent on the special prime). If you can't find the paper, I can look it up later for you.

2008-10-23, 12:11	#14
Pascal Ochem Apr 2006 103 Posts	wblipp cites an old paper (1957) for the result that the largest exponent in an OPN is at least 4. http://oddperfect.org/against.html Has this been improved ? I cannot prove that the largest exponent is at least 5, but I can obtain something like "an OPN containing no exponent strictly greater than 4 must be greater than 10^10000". Last fiddled with by Pascal Ochem on 2008-10-23 at 12:11

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2006-12-15, 13:02	#12
patdumpsite Dec 2003 Albany, NY 2·3 Posts	Has the OPN conjecture been settled? I came across the following: http://arxiv.org/PS_cache/hep-th/pdf/0401/0401052.pdf This paper claims to have settled the nonexistence in 2004, was there a problem found within this publication? I have read nothing about it anywhere but in this paper, but if this was published two years ago, I would have thought that most people would have heard about it by now, which is why I am asking if there was a problem. I am just curous if anyone knows what's going on.

2006-12-18, 14:33	#13
patdumpsite Dec 2003 Albany, NY 2×3 Posts	I did more searching and I came across this thread at sci.math. So I guess people do not seem to believe the proof is correct.

2008-10-23, 13:43	#15
Zeta-Flux May 2003 7·13·17 Posts	Pascal, There was a recent paper that, using sieve techniques, proved that for any given finite set of exponents, there is an upper bound for the first OPN having exponents only in that set (I think even ignoring the exponent on the special prime). If you can't find the paper, I can look it up later for you.