## Re: [PrimeNumbers] OT RE Cardinal of atoms

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• Hi, Yes, an big upper bound because the average of atoms/particle in the interestelar medium is aprox. 1/(cm^3). This would be corrected by the unknown amount
Message 1 of 3 , Apr 30, 2003
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Hi,
Yes, an big upper bound because the average of atoms/particle in the
interestelar medium is aprox. 1/(cm^3). This would be corrected by the
unknown amount of "dark matter". The hypothesis of the Big Bang is
admitted by the majority of physicists, and now the dicovery of the
polarization of the "fosil" radiation reaffirme the BB.
The mass, number and volume of neutrino particles in the Universe
would be introduced if pertinent.
Ignacio

Jose_Ramón_Brox <ambroxius@...> wrote:I think this is a big off-topic, but it could be easy to prove the finitude of atoms (always with based upon the nowadays approved theories)

1) At the beginning it was the Big-Bang, all matter condensed at one point.

2) The age of the universe is believed to be around the 15*10^3 million years. We can state a wide upper bound, say about 10^4 million years.

3) The highest speed for mass-particles is lesser than c=3*10^8 m/s.

4) The smallest atom radius is that of the hydrogen with its electron over the first level: 5*10^(-11) meters.

5) Considering our space as an euclideus one - near true -, the volumen of a sphere is V = 4/3*pi*r^3 with r its radius.

6) With 4) and 5), making a sphere of an atom, it would have a volume around v_atom = 4/3 * pi * [5*10^(-11)]^3 = 5,236 * 10^(-31) m^3

7) Using 2) and 3), supposing and uniform and at-highest-speed expansion, the filled-with-matter-universe radius is R = 10^10 * 365 * 24 * 3600 * c = 9,4608 * 10^25 m.

8) By 5) and 7), the volume of the universe sphere is V_universe = 4/3 * pi * [9,4608 * 10^25]^3 = 3,715 * 10^78 m^3

8) Using 6) and 8), and making the mad supposition that space is fullfilled with the smallest atoms, then if the number of atoms we have is N, roughly it will be V_universe = N * v_atom --> N = V_universe / v_atom = 3,75 * 10^78 / 5,236 * 10^(-31) =7,09 * 10^108 atoms!

Remarking: 10^109 is a big upper bound for the number of atoms in our universe.

So we can do assertions like "factorising a 10^7 bit number will require more than a year of operations if every atom in the universe were a pentium I" and other stuff like this.

Jose Brox

----- Original Message -----
From: Jon Perry
To: Prime Numbers ; Paul Leyland
Sent: Monday, April 28, 2003 9:00 PM
Subject: RE: [PrimeNumbers] Primes vs. Atoms

'> http://web.singnet.com.sg/~huens/paper23.htm
>
> in the Abstract, 2nd sentence:
>
> 'There are more primes than the number of atoms in the universe.'
>
> This a proven fact? I had naturally assumed |atoms| was
> finite, but this sentence makes me question myself.

It's difficult to see how it can be proved. It's easy to prove that there
is a countably infinite number of primes, but by no means easy to prove that
there are a finite number of atoms in the universe or that the statement
even makes sense.

<me>True.</me>

If we restrict ourselves to real atoms in the observable universe, it's
fairly clear that the number is finite (we can only observe a finite volume
and atoms have a non-infinitesimal size) but the number is far from
constant. Atoms are both created and destroyed in large numbers.

<me>True.</me>

If, on the other hand, we include virtual atoms, those which momentarily pop
into and out of existence as a result of vacuum zero point energy
fluctuation it's not obvious to me whether their number is finite, countably
infinite or uncountably infinite.

<me>True.</me>

Where are the theoretical physicists when you need them? David: are you
listening?'

<me>True.</me>

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: Paul Leyland [mailto:pleyland@...]
Sent: 29 April 2003 16:40
To: Jon Perry
Subject: RE: [PrimeNumbers] Primes vs. Atoms

> http://web.singnet.com.sg/~huens/paper23.htm
>
> in the Abstract, 2nd sentence:
>
> 'There are more primes than the number of atoms in the universe.'
>
> This a proven fact? I had naturally assumed |atoms| was
> finite, but this sentence makes me question myself.

It's difficult to see how it can be proved. It's easy to prove that there
is a countably infinite number of primes, but by no means easy to prove that
there are a finite number of atoms in the universe or that the statement
even makes sense.

If we restrict ourselves to real atoms in the observable universe, it's
fairly clear that the number is finite (we can only observe a finite volume
and atoms have a non-infinitesimal size) but the number is far from
constant. Atoms are both created and destroyed in large numbers.

If, on the other hand, we include virtual atoms, those which momentarily pop
into and out of existence as a result of vacuum zero point energy
fluctuation it's not obvious to me whether their number is finite, countably
infinite or uncountably infinite.

Where are the theoretical physicists when you need them? David: are you
listening?

Paul

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