As clued by the flavor text, this puzzle has to do with factoring primes in the complex plane. The image is a 250x250 section of the first quadrant in the complex plane beginning at (0, 0) in the bottom left corner. Each black dot represents a Gaussian prime (a prime number in the ring of Gaussian integers), and each colored dot represents a composite number with exactly two factors.

For each color (red through purple), the composite numbers are factored, and their factors are connected pairwise in the plane by a line as follows:

B: Red

43 + 80i = (8 + 3i)(8 + 7i)

76 + 65i = (8 + 3i)(11 + 4i)

68 + 87i = (8 + 5i)(11 + 4i)

58 + 103i = (8 + 5i)(11 + 6i)

46 + 125i = (8 + 7i)(11 + 6i)

O: Orange

6 + 3i = (2 + i)(3)

12 + 3i = (4 + i)(3)

10 + 11i = (4 + i)(3 + 2i)

4 + 7i = (2 + i)(3 + 2i)

T: Yellow

47 + 140i = (8 + 7i)(12 + 7i)

79 + 100i = (10 + 7i)(10 + 3i)

N: Green

11 + 24i = (4 + i)(4 + 5i)

19 + 34i = (6 + i)(4 + 5i)

31 + 36i = (6 + i)(6 + 5i)

E: Blue

15 + 104i = (6 + 5i)(10 + 9i)

33 + 58i = (6 + 5i)(8 + 3i)

57 + 178i = (10 + 9i)(12 + 7i)

60 + 109i = (11 + 4i)(8 + 7i)

T: Purple

1 + 12i = (1 + 2i)(5 + 2i)

9 + 6i = (3 + 2i)(3)

Taken in order, these letters spell out the solution, BOTNET.