# two

Two is the first even number and the only even prime
number. The word comes from the Greek *dyo* and the Latin *duo* through the Old English *twa*. Early languages often had both feminine
and masculine forms for two and so there are a lot of diverse roots related
to "two-ness". Many "two" words use the Greek root *bi*; biannual,
binary, biscuit, and biceps, for examples. Others come from the Old English *twa*, such as between, twilight, twist, and twin. From *duo* we get dual, duet, dubious (of two minds), duplex (two layers), and double.
The Latin *di* gives us diploma (two papers) and dihedral. The earlier
Greek *dyo* produces dyad, composed of two parts. Two is the only
positive real number that gives the
same result when added to itself as when multiplied by itself. It is conjectured
that 2 is the only even integer that cannot be written as the sum of two
primes (see Goldbach's conjecture)
and it has recently been proved that 2 is the largest value of *n* for which the equation *x ** ^{n}* +

*y*

*=*

^{n}*z*

*has nonzero integer solutions (see Fermat's last theorem). Two is the base of the binary number system.*

^{n}