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Goldbach

Goldbach is a surname of German origin. The best known bearer in mathematics is Christian Goldbach (1690–1764), a Prussian mathematician who worked in Königsberg and Saint Petersburg. In a 1742 letter to Leonhard Euler, he proposed what became known as Goldbach's conjecture.

Goldbach's conjecture, also called the strong Goldbach conjecture, asserts that every even integer greater than 2

A related result is the weak Goldbach conjecture, which states that every odd integer greater than 5

Goldbach's conjecture has influenced and motivated substantial research in analytic and computational number theory, with connections

can
be
expressed
as
the
sum
of
two
primes.
The
two
primes
may
be
the
same,
as
in
4
=
2
+
2.
The
conjecture
remains
unproven
and
is
one
of
the
central
open
problems
in
number
theory.
It
has
been
extensively
tested
by
computer
for
very
large
ranges
and
is
verified
to
hold
for
even
numbers
up
to
at
least
4
×
10^18.
is
the
sum
of
three
primes.
This
statement
was
proven
by
Harald
Helfgott
in
2013,
completing
a
long-standing
line
of
inquiry
in
additive
number
theory.
Despite
this
breakthrough,
the
strong
conjecture
concerning
sums
of
two
primes
remains
unresolved.
to
prime
distribution,
the
circle
method,
and
the
study
of
prime
gaps.
The
name
continues
to
be
used
in
discussions
of
prime
representations
and
related
problems
in
mathematics.