Elusiveness is subjective, but there's certainly plenty of patterns to be found (though, to be fair, what constitutes a pattern might also be subjective). You should check out Terence Tao's blog [0], he's not only one of the most prominent mathematicians in the field but he's also excellent at explaining things. These slides [1] for example don't require any background in math.

[0] https://terrytao.wordpress.com

[1] https://www.math.ucla.edu/~tao/preprints/Slides/primes.pdf