Today is the 40th day of the year, and I did 40 of each this morning, and likewise I did 39 of each yesterday morning. I went through a period where it was getting harder, so I broke the routine up into part that was done in the morning and part in the evening, but as of yesterday I'm finding it easy to do it all in one go in the morning, which is really satisfying.
Typical prescribed exercise routines grow exponentially (e.g., by 10% a week). By that measure, increasing by 1 nth on the nth day is a bad idea: in the first week, taking 1 as the baseline, you're going up by 700% a week, and by the 52nd week, you're down below 2%/week; and normally you're supposed to only do alternate days with anaerobic exercise. I figured I might hit the baseline level my body was up for some time between 20 and 70 and crap out because I was going too fast, but that if I didn't, I'd get over that hill and reach a point after which the percentage growth rate was a joke. I was OK with that, but for this reason (and many others) I can't recommend this for people who are trying to develop the optimal exercise routine.
That said, it's the first time I've maintained a scheduled exercise routine anything like this long. I think this is because it is simple enough to remember (I never have to look anything up in order to get my routine started, as I would with something more thoughtfully structured like the 100 Pushups regimen or Body For Life) and requires no measurement other than counting, but involves obvious daily progress so I can feel like I am accomplishing something.
Supplementing that motivation is the interesting question of how to break the workout up into sets: I get lactic-acid pain after 10-15 right now, which means I should take a short break about that often. Successive numbers necessarily always have rather different factorizations, and primes can't be factored at all, so there's a certain amount of creativity involved and also room to regulate how much I am challenging myself on a given day, which helps make sure I can complete the routine even if things are not optimal (e.g., if my joints hurt or I'm full).
The one cheat I've used was that, if I wasn't up to the situps, I could do 2x as many crunches. I used this twice, I think, around days 20-30; I'm very cautious with ab strain because I disabled myself for a couple weeks a few years ago when I spontaneously decided to see how many situps I could do and pushed through some warning signs.