Boeing numbered their designs numerically starting with 1. However, as you can guess, many designs never got beyond the conceptual stage, so there a numerous gaps. However, until the jetliners, the aircraft were hardly ever known by their numbers. The Monomail began as the 200, and later was produced as the 221. The 247 was known by its number, but was overshadowed by the DC-2 and DC-3. The Stratoliner, derived from the B-17(Boeing model 299) started as the 300, and evolved to the 307. The "Clipper" flying boats were model 314, and the aforementioned 377 was the Stratocruiser. When Boeing began work on the design for their first commercial jet, they had reached the 700's, and because 7 is thought by many as a lucky number, previous Boeing commercial airliners had ended with a 7, and because it was symmetrically pleasing, Boeing decided on the number 707. After that, the trend was to keep the bookend 7's, and increase the middle digit. The exception has been the 720, which was desigend originally as a 707 derivative, to be called the 707-020, as it was smaller than the 707-120. However, "Pat" Patterson, the head of launch customer United, had said that he would not by the 707, so Boeing had to change the model number. The first idea was to use 717, which had also been used for the KC-135. But Patterson again objected; for some reason he did not like the final 7. This is strange, because United had operated the Boeing 247 and 377, as well as the DC-7, but Boeing agreed and changed the name to 720. However, the idea of the 7x7 was continued, and United purchased every subsequent model, being a launch customer on the 727, 737, and later (long after Patterson retired) the 767 and 777. And now Boeing has again reused 717 for the inherited DC-9 derivative that began life as th MD-95.
"So many planes; so little time..."