A Goldbach partition of an even integer is an unordered pair of primes such that (Oliveira e Silva). Letting denote the number of Goldbach partitions of without regard to order, the number of ways of writing as a sum of two prime numbers taking
the order of the two primes into account is
(1)
The Goldbach conjecture is then equivalent to the statement that or, equivalently, that , for every even integer .
A plot of ,
sometimes known as Goldbach's comet, for up to 2000 is illustrated above.
The following table summarizes the values of several variants of for , 4, ....
is an unordered pair of primes 
such that 
(Oliveira e Silva). Letting 
denote the number of Goldbach partitions of 
without regard to order, the number of ways of writing 
as a sum of two prime numbers taking
the order of the two primes into account is
or, equivalently, that 
, for every even integer 
.
,
sometimes known as Goldbach's comet, for 
up to 2000 is illustrated above.
for 
, 4, ....
1 or prime
prime
odd prime
." Math. Comput. 61, 931-934,
1993.Sloane, N. J. A. Sequences