'''Goldbach's comet''' is the name given to a plot of the function '''g(E)''', the so-called '''Goldbach function'''.

The Goldbach function is studied in relation to Goldbach's conjecture. The function '''g(E)''' is defined for all ''even'' integers '''E>2''' to be the number of different ways in which E can be expressed as the sum of two primes. 

;Examples

* G(4) = 1, since 4 can only be expressed as the sum of one distinct pair of primes (4 = 2 + 2)
* G(22) = 3, since 22 can be expressed as the sum of 3 distinct pairs of primes (22 = 11 + 11 = 5 + 17 = 3 + 19)


;Task

* Find and show (preferably, in a neat 10x10 table) the first 100 G numbers (that is: the result of the G function described above, for the first 100 even numbers >= 4)
* Find and display the value of G(1000000)


;Stretch
* Calculate the values of G up to 2000 (inclusive) and display the results in a scatter 2d-chart, aka the [https://upload.wikimedia.org/wikipedia/en/f/fb/Goldbachs_comet.gif Goldbach's Comet]


;See also
;* [[wp:Goldbach's conjecture|Wikipedia: Goldbach's conjecture]]
;* [[oeis:A045917|OEIS: A045917 - From Goldbach problem: number of decompositions of 2n into unordered sums of two primes]]