>From: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]>
>To: [EMAIL PROTECTED]
>Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture?
>Date: Tue, 21 Mar 2000 15:59:34 -0500
>
>At the new gigahertz speed, it would not take that long to check out all
>even numbers, would it? :-) :-)
>
>Or find an exception less than 10^100 or so.
Okay, your first statement is obviously intended flippantly.
The second, OTOH, looks good on the surface. However, even assuming that we
can check a trillion (I am using the American meaning of trillion,
1,000,000,000,000= 1000 billion = 1 million million, or 10^12) even numbers
per second on one computer for each person on Earth, it will take
(5*10^87)/(6*10^9) seconds to check them to one googol (the pseudoformal way
of stating 10^100).
This is equal to 8.33*10^77 seconds.
I will abbreviate this number and future numbers as 8.33E87, since it is
easier to type.
8.33E77 seconds
2.31E74 hours
9.65E72 days
1.38E72 weeks
2.94E70 years
This is about eight thousand times as many years than there are atoms in the
sun:
2E30 metric tons = 2E42 grams = 1.2E66 atoms of pure hydrogen-1, which the
sun is not.
We can certainly attempt to find a counterexample, and I would not be
surprised if an idle-time project to do just this were started. However, I
would be highly surprised if the search (if unsuccessful) made it into the
googol range, especially since finding even one probable prime, yet alone
two, takes more than one clock cycle, and a terahertz processor (which is
what I figured on) would certainly overheat in seconds if it were made of
current materials.
Giving a computer to every person on the planet, OTOH, is an admirable goal,
and one that would benefit mankind in far more ways than disproving the
Goldbach Conjecture would.
Quantom computing might be adapted for this, but there is so much hype on
that topic that it is hard to know what the truth is.
Regards,
Nathan Russell
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