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centered heptagonal n.  and  strong prime

First numbers that belong to both sets:

71, 197, 1471, 2647, 3697, 5741, 10781, 12391, 14561, 18397, 29947, 50821, 54251, 68111, 72073, 76147, 89041, 104147, 114031, 124363, 139301, 150697, 202441, 230273, 299447, 339613, 357281, 432433, 465011, 485647, 547471, 581197, 584053, 595547, 630701, 654697, 688423, 691531, 700897, 726181, 742211, 764947, 781397, 808081, 835213, 901447, 933703, 973897, 1022491, 1037681, 1127197, 1143143, 1175371, 1195741, 1378147, 1382543, 1395773, 1431361, 1503881, 1559447, 1732193, 1756903, 1791791, 1837151, 1893361, 2024261, 2083243, 2104901, 2154041, 2310547, 2425697, 2443211, 2615761, 2664397, 2688883, 2738191, 2756797, 2781703, 2812993, 2857093, 2882447, 2991451, 3089311, 3475543, 3552697, 3637831, 3818431, 4055983, 4108903, 4139297, 4177447, 4394321, 4417883, 4520713, 4640833, 4673131, 4705541, 4811647, 4977197, 5213671, 5316697, 5351263, 5490647, 5694151, 5983447, 5992603, 6140051, 6516511, 6670231, 6738047, 6904171, 7062371, 7212311, 7373983, 7414681, 7661221, 7869751, 7880251, 8006797, 8295211, 8742931, 8954401, 9010471, 9134441, 9225133, 9327697, 9546083, 9790397, 9825551, 10120951, 10168621, 10252313, 10700383, 10934197, 11346301, 11396771, 11599771, 11650801, 11689147, 11907631, 11946397, 11998183, 12219523, 12311251, 12535447, 13111561, 13562473, 13672933, 14049043, 14730283, 14975423, 15310303, 15368921, 15841897, 15961261, 16096081, 16337161, 16382563, 16625771, 16702141, 17805481, 17947861, 18074897, 18394447, 18506951, 18830281, 19041947, 19238381, 19485341, 19750501, 20286197, 20421241, 20488931, 21379093, 21465683, 21936293, 21953821, 22076713, 22094297, 22874923, 23451163, 23523697, 23650901, 23723743, 23814953, 24108001, 24402841, 24458323, 24532397, 24923123, 25732813, 26190361, 26286191, 26671261, 26903647, 26981333, 27195547, 27351871, 27528271, 27606853, 27685547, 28080697, 28219661, 29506093, 29607803, 29832181, 30655241, 31091831, 31910831, 32271163, 32612147, 33040897, 33126983, 33906797, 34234397, 35049211, 35204443, 35382271, 35404531, 35649853, 36210553, 36752941, 37093981, 37185191, 37757791, 38011121, 38381113, 38497103, 39032911, 39501841, 39619511, 39879001, 40281697, 40734163, 40829741, 41045201, 41888491, 41912711, 42593713, 43749161, 44970241, 45146053, 45878071, 46564897, 47411281, 47927951, 48525583, 48760447, 49153147, 49258133, 49284397, 49363231, 49784743, 49916833, 51623041, 51919183, 52135091, 52270261, 52351447, 52568251, 52785503, 53030447, 53357921, 53467303, 54429173, 54456781, 55093697, 56014001, 56210197, 57139741, 57366233, 58019893, 59424821, 60090073, 60206147, 60351397, 61138771, 61168031, 62580743, 63740447.

Some larger examples :