"Many people believe, King Gelon, that the grains of
sand are infinite in multitude; and I mean by the sand not only that
which exists around Syracuse and the rest of Sicily, but also that which
is found in every region, whether inhabited or uninhabited. Others think
that although their number is not without limit, no number can ever be
named which will be greater than the number of grains of sand. But I
shall try to prove to you that among the numbers which I have named there
are those which exceed the number of grains in a heap of sand the size
not only of the earth, but even of the universe."

—Archimedes,*The Sand Reckoner* (opening sentences)

—Archimedes,

In Archimedes'
The Sand Reckoner, addressed to
Gelon, King of Syracuse, he attempted to count the number of grains of
sand required to fill the entire universe. Assuming that one poppy-head
would not contain more than 10,000 grains of sand, and that its diameter
is not less than ^{1}/_{40}^{th}^{7}
times the sphere exactly
containing the orbit of the sun as a great circle, he found that the
number of grains of sand required to fill the universe turns out to
be less than
10^{63}.
In order to perform this feat, Archimedes had to invent a notation
for expressing these large numbers.

This is a unique and extraordinary achievement for Archimedes' time. The ancient Greeks had little interest in numbers outside of geometry.

Nowadays, the total number of *particles* in the universe
has been variously estimated at numbers from
10^{72} up to
10^{87}.
The total number of atoms in your body is about
10^{28}.
If the universe were packed solid with neutrons, there
would still be only
10^{128}
particles, a number larger than a
googol but much smaller than a
googolplex.

You don't need huge volumes of particles to get a glimpse of large numbers, however. All you need is combinatorics. How many ways are there to arrange 30 books on a bookshelf? The answer is 30 factorial (which is abbreviated 30!), or 265,252,859,812,191,058,636,308,480,000,000.

Mathematicians often have to use really big numbers in their work. There is much interest in finding huge numbers with certain properties. Examples are odd perfect numbers (none of which has yet been found) and Mersenne primes,

If you're interested in getting a further perspective on the size of the universe, see Universe facts on our sister site, All Fun and Games. You may also find more facts about large numbers there.