shadowcrust wrote:until we explore the limits of the variable storing the score...

An unfortunate incident revealed some clues about the likely limits of the highest high score in FTL. Instead of continuing a game, this screen popped up:

I dreaded that it was a sign of a corrupted profile, and right I was:

All ships, stats and achievements were deleted, replaced by some insanely high session stats. I suspect this number, 32766, is the highest value that can be stored in the respective variables (ships defeated, beacons explored, scrap collected, and crew hired). It is almost 2 to the power of 15 (32768) and is apparently the maximum number of some data types (very close to the maximum value an integer variable can hold, for example).
If the score formula is used (ships defeated x 20, beacons visited x 10, scrap x 1), then it adds up exactly to the 1015746 score displayed above. Although the game was played on hard, the formula used is for easy mode.
Defeating 32766 ships on hard is conceivably possible, that would score 982980 points (30 points each ship). Exploring 32766 beacons is out of the question, as only beacons count towards that number which are not overtaken by rebels. In a very good game, discovering the hidden sector, 130 explored beacons are about the limit, I'd wager, at least I've never seen a higher number for beacons explored. That would add an insane score of 1950 (130x15) towards the total score on hard. Scrap collected would peak at about 3000 on hard, although I've never come very close to this myself (2634 on hard). That's another 4500 points, in total such an extraordinary game would add up to 989430 points, just short of a million. Going over a million points legitimately is impossible, unless 32766 ships defeated was not the maximum value the variable can hold.