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centered heptagonal n.  and  weak prime

First numbers that belong to both sets:

43, 463, 547, 953, 1933, 2843, 4663, 8233, 9283, 11173, 20483, 29303, 34651, 37493, 41203, 46691, 56897, 57793, 65213, 84631, 93563, 112771, 158047, 168631, 187573, 207523, 216133, 244861, 252323, 257993, 289297, 297403, 305621, 307693, 316051, 333103, 368551, 384623, 393961, 415381, 425083, 472697, 475273, 506731, 528263, 536453, 569843, 592663, 607153, 627733, 639647, 676061, 729373, 751913, 859321, 873251, 876751, 959183, 977593, 1018711, 1064533, 1083923, 1159201, 1163233, 1262101, 1295953, 1325941, 1330253, 1400197, 1453831, 1467397, 1508473, 1540813, 1601783, 1712551, 1717451, 1751947, 1796803, 1934773, 1976633, 1997731, 2040263, 2045611, 2067073, 2192653, 2259643, 2265271, 2327641, 2373533, 2419873, 2466661, 2472541, 2543647, 2633947, 2640023, 2682751, 2707321, 2787947, 2838151, 3122281, 3202123, 3228961, 3249163, 3303343, 3385453, 3392341, 3419963, 3531571, 3559753, 3580963, 3616453, 3673601, 3781961, 3789241, 3995923, 4116491, 4238851, 4269721, 4449397, 4457293, 4902353, 5171041, 5282243, 5420731, 5446897, 5552191, 5587513, 5631823, 5658493, 5801797, 5946893, 6056891, 6130783, 6205123, 6214447, 6317473, 6506963, 6545197, 6554773, 6815971, 6825743, 6894343, 7052431, 7303031, 7333397, 7384147, 7506661, 7547723, 7588897, 7754713, 7838293, 8338373, 8831663, 9044197, 9100547, 9145753, 9191071, 9270647, 9316273, 9465331, 9592381, 9650411, 9731947, 9837283, 9872521, 9978613, 10300291, 10444897, 10897111, 11183047, 11195563, 11245697, 11384143, 11548853, 11804563, 12102091, 12363821, 12429691, 12588493, 12628351, 12681593, 12734947, 12841991, 12962951, 13016893, 13125113, 13274647, 13342897, 13507411, 13617647, 13728331, 14105197, 14161463, 14288471, 14515663, 14558461, 14672897, 14802173, 14917561, 15076951, 15135121, 15856793, 16036091, 16156183, 16686853, 16993943, 17009371, 17133047, 17179541, 17742383, 17821273, 18700613, 19156411, 19700647, 19767133, 19967263, 20034197, 20151601, 20218843, 21171991, 21240913, 21327223, 21726503, 21796321, 22024003, 22288183, 22429723, 22714147, 22731983, 22803397, 23018311, 23869763, 23888047, 24181543, 24606583, 24699473, 24829813, 25129021, 25222891, 25298113, 25808791, 25827803, 25903921, 26037397, 26132947, 26594023, 27039671, 27137041, 27215063, 27293197, 27744641, 27764353, 27981647, 28160063, 28398833, 29181797, 29202013, 29934451, 30180613, 30262891, 30489733, 30841973, 31321753, 32016601, 32101343, 32249911, 32334961, 32420123, 32505397, 33450803, 33645851, 33710993, 33797947, 33819703, 34081321, 34783897, 35027063, 35115697, 35471353, 35493641.

Some larger examples :