First 1e6 integers, represented as binary vectors indicating their prime factors, and laid out using the sparse matrix support in @leland_mcinnes's UMAP dimensionality reduction algorithm. This is from a 1000000x78628 (!) binary matrix. Very pretty structure emerges. 
Details: for each i up to n, find prime factors of i. For each i, make binary vector with π(n) columns, 1=prime factor present, 0=absent and stack into matrix. Lay out with UMAP, using cosine similarity. Code: gist.github.com/johnhw/dfc7b8b…
Filtering the numbers by parity: even is green; odd is orange
And, as might be expected, the primes are diffuse cloud near the centre (white=prime, nonwhite=composite).
Finally for now, a plot coloured by number of prime factors (black= prime, lighter = more unique prime factors)
For fans of false colour multispectral images: coloured by prime factor, with hue mapped to (log) prime value. Redder=small prime factors, bluer=large prime factors. Small amount of noise artificially injected to make colours clearer.
The "big bang". A video of the first million integer layout, in sequence:
