Is it pure coincidence that e in decimal repeats four digits near the beginning?

Is it useless noise to note that e in decimal repeats four digits near the beginning? From the Ruby interpreter, I get that e ~= 2.71828182845905 . Let me insert some commas to emphasize the repetition I noticed: 2.7,1828,1828,45905 . We see a repetition of 1828, with the first instance starting only one digit past the decimal point, and the second one immediately afterward. Does this say something profound about 10, the base of our number system? Or is it just a useless and irrelevant observation, like noting that some ratios in dimensions taken on an ancient pyramid are within .01 of some ratios of dimensions taken on some randomly chosen bicycle?