This is the Book of Numbers. And there are a lot of numbers:

603,550 is a nice round number, which could happen, but we notice that all the individual tribes' counts are also round numbers, either exact multiples of 100 or (in the case of גד) a multiple of 50. That’s more than a coincidence. Clearly the counts were rounded. That may simply be a reflection of the fact that it’s humanly impossible to count that exactly, but the Torah elsewhere uses exact numbers:

Rav Yaakov Kaminetsky has an intriguing idea. He notes that ה׳ tells Moshe the reason for the census: תפקדו אתם לצבאתם.

And the army was organized under שרי המאות and שרי חמשים:

Each שר חמשים had his חמשיו, his platoon:

So Rav Kaminetsky understands the rounding to reflect this organization. It wasn’t so much that 603,550 people were counted; it’s that 12071 (exactly) platoons were set up, and that multiplied by 50 is 603,550.

That’s interesting, but there’s a bigger problem with that number: it appears much earlier in chumash:

And that was from the building of the Mishkan, 7 months earlier.

So Rashi says that the census was by cohorts, which fits the military model. Everyone who was 20 as of א׳ תשרי was drafted and thus counted, leaving out all those who turned 20 during the year. But Ramban is still bothered.

So he ends up concluding that the two numbers represented two different populations, and the fact that they are the same is simply a coincidence.

It’s too much of a coincidence for me to accept.

Mizrachi points out that the fact that no one died in those months would be a miracle, but there were a lot of miracles at that time, so it’s not that much of a difficulty:

But the objection that the Levites weren’t included in the second count seems like an insurmountable problem.

The Maharal solves it with a radical idea. He goes back to the command to collect the מחצית השקל:

Rashi (based on the gemara) sees a hint to three different collections of silver:

The Maharal says that Rashi is overcounting his counts:

We still need to assume two miracles: one, that no one died in the interim, and two, that everyone’s papers were in order. Everyone who gave their מחצית השקל ancipating being counted actually was correctly counted. Knowing how elections and registrations work, that seems like the bigger miracle.