Major breakthrough in understanding prime numbers

A recent study indicates we might be able to predict the next prime number.

I've read the paper, and can assure you there is no breakthrough in there. It's just phrasing primes and related functions in terms of a wheel sieve with basis {2,3,5,7} [1]. [1] https://en.wikipedia.org/wiki/Wheel_factorization

The internet as we know it would quite literally break if someone were to discover any sort of function that can return the first N primes, no matter what kind of function it may be. However I hardly understand how the wheel factorization works at all, though. How is deterministically assigning prime numbers to four buckets going to solve the task?

Not 4 buckets, but 48 buckets, since primes > 7 cannot be divisible by 2,3,5,7, leaving only 1 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 209 as possible remainders modulo 2*3*5*7 = 210.