Your question already garnered a ton of answers but I still want to try: the distribution of primes has a deep connection to the Riemann Zeta function. RZF and

Your question already garnered a ton of answers but I still want to try: the distribution of primes has a deep connection to the Riemann Zeta function. RZF and it's hypothesis is indeed one of the millennium problems, but beyond (or maybe, because of) that, RZF connects number theory and complex analysis (and probably more such as group theory, but I don't want to risk saying anything incorrect) at a very deep level. So picking off little morsels of the bigger problem is kind of the first steps towards climbing this metaphorical mountain.