(Last updated 4/6/2022)
Of the "main" US highways (i.e. the one- and two-digit routes), the longest nine were all east-west routes (6, 20, 50, 30, 40, 60, 70, 80, 12). And if we take the longest 16 highways, only one of them is a north-south route (US 1, shown in red here):
That stands to reason, because the United States is roughly twice as wide from east to west as it is from north to south. So it makes sense that there would be more long east-west routes.
Not really. The three longest branch routes are all north-south highways (287, 281, and 191). The fourth-longest (160) does run east-west, but it is about 400 miles shorter than the longest north-south branch routes. The next three longest also run north-south (395, 183, 385):
So, if the longest main routes run east-west, then why do the longest branch routes run north-south?
The following assumes you are familiar with the methodology that was originally used to assign US route numbers (if not, then you might benefit from this quick primer). With that in mind, there were 50 (give or take) numbers available for main east-west US routes (evens from 2-98), and 50 for north-south routes (odds from 1-99). But as mentioned previously, the 50 odd numbers had to be spread out over a distance roughly twice as wide as the distance that the 50 even numbers had to cover.
The 50 even numbers were more than enough to cover the main east-west routes. In fact, nine of the even numbers were not immediately assigned in 1926 (44, 46, 56, 58, 62, 82, 86, 88, 98). The majority of those numbers did end up being used sometime after the original routes were established, although only two of those highways are of considerable length, and two of the numbers (86 and 88) have never been assigned at all.
Similarly, nine of the 50 odd numbers were not immediately assigned either (33, 35, 37, 39, 43, 47, 57, 59, 79). Presumably that was intentional, to save some numbers for future US routes (and indeed, six of those numbers were assigned later, although 37, 39, and 47 have never been used). But unlike the even numbers, the odd numbers were not distributed evenly across the width of the country. Rather, they were heavily weighted towards the eastern half of the nation.
As an example, the north-south route corresponding to the centerline of the nation is US 81. So for the western 50% of the country, only 20% of the odd numbers were left to be assigned to the remaining north-south routes. That was certainly intentional, because the population density was (and still is) much higher in the eastern half of the U.S. But as population increased in the West and new north-south routes were added to the system, no appropriate two-digit numbers remained to be assigned. So the gaps were instead filled with three-digit numbers, many of which eventually attained lengths substantially greater than that of most east-west branch routes.
Not only is US 287 the longest 3-digit US route, but by virtue of the fact that it runs diagonally, it also intersects five of the six next-longest 3dus routes (as illustrated on the map above). Following are a few photos of these junctions, arranged from southeast to northwest. First, US 287 and US 281 intersect (and share a brief overlap) in Wichita Falls TX:
Today US 281 and US 287 run along newer freeways, but formerly the two routes joined on surface roads through the downtown area, as shown in this historic photo:
Not far from there, between Vernon and Oklaunion TX, US 287 and US 183 share a nine-mile overlap. This concurrency also includes US 70, which makes it interesting because the three routes are signposted with three different cardinal directions:
Continuing to the northwest, US 287 intersects US 385, and in fact shares a 95-mile-long overlap with it between Boise City OK and Lamar CO:
Approximately in the middle of that overlapping segment, US 287-385 intersects US 160 at the south edge of Springfield CO:
And finally, much farther to the northwest, US 287 joins with US 191 at Moran Jct. WY:
The two routes share pavement for 104 miles, not diverging again until a few miles north of West Yellowstone MT (although about 67 of those miles are on a segment that passes through Yellowstone National Park, where US routes are not signposted and technically do not exist).