spaf@gatech.UUCP (Gene Spafford) (02/18/84)
There was an article in the paper the other day about how some
computer scientists had used a computer program to disprove
Merten's Conjecture. They had found that the first 10 billion
numbers met the conjecture, but there was an instance beyond
this that disproved the conjecture. It also stated that
Merten's Conjecture had stood for 99 years.
My question: what is Merten's Conjecture? Anybody know anything
about this? Thanks.
--
Off the Wall of Gene Spafford
The Clouds Project, School of ICS, Georgia Tech, Atlanta GA 30332
CSNet: Spaf @ GATech ARPA: Spaf.GATech @ CSNet-Relay
uucp: ...!{akgua,allegra,rlgvax,sb1,unmvax,ulysses,ut-sally}!gatech!spaftimw@umcp-cs.UUCP (02/20/84)
In response to Gene's question:
According to the Washington Post, my local source of knowledge,
Mertens Conjecture is that a special summation function (I don't
know what) derived from the prime factors in a number is always
less than the square root of that number.
It says that Mertens was able to prove this with pencil & paper
for the first 10,000 integers. In 1913 another mathematician
proved it up to 5,000,000 and a computer proved it to
10,000,000,000 in 1963. Now these two guys are saying that they
disproved it at some outrageously large number with many,many zeros.
But I have a question also. They say that they disproved the theorem
but they probably will not know the number because of the size of it.
If this is true, then how do they that the theorem doesn't work??
The Post also quotes " Both people belong to a computer
network that allowed them to echange their latest work over
transalantic telephone line......" Hmmmmmm
--
Speaking: Tim Wicinski
University of Maryland
UUCP: {seismo,allegra,brl-bmd}!umcp-cs!timw
CSNet: timw@umcp-cs ARPA: timw.umcp-cs@CSNet-Relay