Maybe try doing curls with 3/5 pound weights instead! Or standing shoulder presses. Do that for a few weeks and then return to pushups. At that point you'll be strong enough to do 1. And then as you say, 1 becomes 2, 2 becomes 5, and 5 becomes 100. I couldn't do more than 15 in a row on January 1. On August 16 I did 525 in 2.5 hours (I know this because it is in my Google Sheet).