A pair of primes
that sum to an even integer are known as a Goldbach partition (Oliveira e Silva).
Letting
denote the number of Goldbach partitions of without regard to order, then 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, ....
that sum to an even integer 
are known as a Goldbach partition (Oliveira e Silva).
Letting 
denote the number of Goldbach partitions of 
without regard to order, then 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