Re: Conjectures with very large lowest counterexamples
From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 07/05/04
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Date: 05 Jul 2004 22:36:22 +0300
larrylard@hotmail.com (LarryLard) writes:
> Are there any seemingly-plausible conjectures which are currently
> known to fail, and fail for the first time at 'large' values?
Maybe google for the law of small numbers. (The false deduction that
as it's true for a small run of integers it must be true for all integers.)
IIRC there's a famous family of non-theorems of the form
gcd(n^a+b, (n+1)^a+b)=1 for all n
Some choices of a and b have a run of 1s that is enormous before the
first counterexample.
Phil
-- 1st bug in MS win2k source code found after 20 minutes: scanline.cpp 2nd and 3rd bug found after 10 more minutes: gethost.c Both non-exploitable. (The 2nd/3rd ones might be, depending on the CRTL)
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