Home

643

643 is a natural number that lies between 642 and 644. In decimal notation it is written as 643, and it is an odd prime number.

In number theory, 643 is prime since no integer between 2 and 23 divides it. The square

Representations of 643 include its Roman numeral and common base conversions. In Roman numerals it is written

In mathematical contexts, 643 is often cited as an example of a small prime with 4k+3 congruence.

root
of
643
is
approximately
25.3,
so
divisibility
tests
for
all
primes
up
to
23
fail.
As
a
prime
congruent
to
3
modulo
4
(643
≡
3
mod
4),
it
cannot
be
expressed
as
a
sum
of
two
integer
squares.
as
DCXLIII.
In
binary
it
is
1010000011,
and
in
hexadecimal
it
is
0x283.
It
appears
in
lists
of
primes
and
in
discussions
of
modular
arithmetic,
illustrating
properties
that
arise
for
primes
in
the
4k+3
class.
Beyond
pure
mathematics,
643
may
be
encountered
as
a
numeric
identifier
or
data
value
in
various
coding
and
cataloging
systems,
though
it
does
not
have
a
widely
recognized
meaning
outside
numerical
contexts.