I've run some samples at 577#, and after a few residue sets that left 16 numbers coprime to 577#, I was lucky to get one that left only 13 coprimes:

Code:

k=57038838199945595943092978020969218682105458339028727587781701358714381875907979834149194637905736734686560196824691232279743998298569591278748933757883925287649006675231123018149656337436046099711266218991008707108800654609166747134268
coprimes to 577# in range [k, k+2310] for k+x, x=
425
521
665
695
701
733
743
793
833
859
941
1393
1769

On the downside, none of the differences between all these numbers divide a prime > 577, so it takes one more prime for every open residue to cover the whole set.

Thus, proceeding at this point, and taking into account the mirror image pattern, there are 12,454,041,600 possibilities in total to cover a whole 2310-range at 653#. One of those possibilities is given by the offset number

Code:

84014187931330891982928862151585423133277701808931254622654423525808390988632742949399274570817791940040095608793771771564891142528915498180659440098040141622958738285319473714869936965247261697018313728314093388024245806686921131025648923863267854404228281265796338542408