You can test it quite easily, but base doesn't seem to make a difference. There are some patterns that emerge when considering the primes spatially, though.
Elsewhere someone already mentioned the Ulam Spiral [1] and I'll add the Sieve of Pritchard [2] which combines the Sieve of Eratosthenes with Wheel Factorization. Its wiki page has a nice visualization. Notice that when the primes are arranged in a rectangular grid (rows at a time, left-to-right, top-to-bottom) there are entire columns that can immediately be eliminated from consideration.
