One of the questions that may be asked about our new year is whether 2013 is composite or prime -- that is, whether it does or does not have factors other than 1 and the number itself. A shortcut useful here is this test for divisibility by 3 (offered as a 5x5 square):
An integer is
3 if and only
if the sum of its
digits is also.
And so, since 2 + 0 + 1 + 3 = 6 (which is divisible by 3), then 2013 is divisible by 3. Indeed, the prime factorization is 2013 = 3 x 11 x 61.
My email on this New Year's morning contained a gift -- "Digits" -- a poem that compares numbers with nature, from Virginia poet and dream specialist Joan Mazza; she has given me permission to post it here.
Digits by Joan Mazza
A second look at the oldest fossils
of early vertebrates and you’ll see
seven digits, or eight, not five. Devonian
tetrapods all had more than five digits
ending their primitive limbs. In evolution,
who wins the lottery of millions
of descendants in the future family
tree, instead of extinction’s blind end,
may only catch a bit of luck, not always
adaptive advantage. Let’s count
ourselves fortunate that our number
systems aren’t based on fourteen
phalanges, instead of base ten. Just
calculate how differently we’d measure
everything. Called a TEN, you’d
be barely average. No prize. Those
with only five would hide hands
and feet, afraid of being cast aside
by others’ pointing and whispers,
shunned, confined to reside in small
and separate villages with their kind,
to wear their narrow shoes and gloves.