[oifwkfic] Deeply analyzing a range of integers

Pick a range of consecutive integers and test the primality of all of them.

Or give the smallest prime factor of all of them, perhaps giving up if a small one cannot be found within a given threshold of computation effort (easy to do for the elliptic curve method).

Or the complete factorization of all of them.

Not just factorization but also RPPFN.

Or, instead of a range of consecutive integers, uniformly randomly sample among all N-bit numbers.

This gets computationally difficult for wide ranges, and for large integers.  What would be useful as raw data for research by others?

Inspired by the Hubble Deep Field and successors, which observed "deeply" a small region of the sky (revealing many galaxies), providing astronomers a rich data set for research.  Perhaps a "deep field" of "distant" integers will reveal previously never-before-noticed weirdness.