Goldbach's comet

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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 Goldbach's Comet

See also

Wikipedia: Goldbach's conjecture

Arturo

<lang rebol>G: function [n][

   size select 2..n/2 'x ->
       and? [prime? x][prime? n-x]

]

print "The first 100 G values:" loop split.every: 10 map select 4..202 => even? => G 'row [

   print map to [:string] row 'item -> pad item 3

]

print ["\nG(1000000) =" G 1000000]

csv: join.with:",\n" map select 4..2000 => even? 'x ->

   ~"|x|, |G x|"

write the CSV data to a file which we can then visualize
via our preferred spreadsheet app

write "comet.csv" csv</lang>

Output:

The first 100 G values:
  1   1   1   2   1   2   2   2   2   3 
  3   3   2   3   2   4   4   2   3   4 
  3   4   5   4   3   5   3   4   6   3 
  5   6   2   5   6   5   5   7   4   5 
  8   5   4   9   4   5   7   3   6   8 
  5   6   8   6   7  10   6   6  12   4 
  5  10   3   7   9   6   5   8   7   8 
 11   6   5  12   4   8  11   5   8  10 
  5   6  13   9   6  11   7   7  14   6 
  8  13   5   8  11   7   9  13   8   9 

G(1000000) = 5402

Here, you can find the result of the visualization - or the "Goldbach's comet": 2D-chart of all G values up to 2000