Thread: Covering sets View Single Post
 2016-03-02, 17:52 #7 mart_r     Dec 2008 you know...around... 26C16 Posts 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 Last fiddled with by mart_r on 2016-03-02 at 18:37 Reason: typo