🚀 go-pugleaf

Hmm, I seem to recall an article on this subject in "Scientific
American", probably in one of Martin G's mathematical columns.
Unfortunately since it was back in the 70's or 80's and I don't have
my collection to hand I can't give you a precise reference just now.

However, in the article he explores just such an 'infinite pathway' as
you described with the numbers arranged in a spiral. Again long lines
of primes appeared which were likened to gold bearing loads in a
goldmine. If I recall M.G. speculated on whether the prescence of
these loads could prove useful for finding large primes, I think he
invited readers with computers to investigate what happens to the
density of these primes bearing loads at increasing distances from
zero.  Now is your chance to find out... there are an infinite number
of primes, so are there an infinite number of these lines?