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centered heptagonal n.  and  twin primes

First numbers that belong to both sets:

43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, 41203, 57793, 68111, 84631, 104147, 139301, 168631, 207523, 244861, 307693, 333103, 357281, 415381, 465011, 475273, 506731, 592663, 595547, 607153, 729373, 742211, 781397, 876751, 977593, 1018711, 1037681, 1159201, 1163233, 1262101, 1325941, 1503881, 1508473, 1559447, 1712551, 1791791, 1796803, 2024261, 2045611, 2067073, 2154041, 2192653, 2265271, 2327641, 2419873, 2425697, 2443211, 2472541, 2707321, 2838151, 2882447, 3122281, 3228961, 3303343, 3531571, 3789241, 3995923, 4139297, 4394321, 4705541, 5171041, 5420731, 5490647, 5552191, 5658493, 6130783, 6140051, 6317473, 6554773, 6815971, 7052431, 7754713, 7838293, 9191071, 9465331, 9592381, 9790397, 9825551, 9837283, 9872521, 10897111, 11396771, 12429691, 12588493, 12628351, 13016893, 13728331, 14515663, 14558461, 14917561, 15368921, 16156183, 16625771, 18074897, 18506951, 19041947, 19156411, 19485341, 19767133, 19967263, 20286197, 20488931, 21171991, 21327223, 21796321, 22024003, 22094297, 24532397, 24606583, 25129021, 25298113, 25808791, 25903921, 26286191, 26594023, 27685547, 29202013, 29934451, 30180613, 30489733, 30655241, 31091831, 31321753, 32016601, 32249911, 32612147, 33906797, 34234397, 35851201, 36730261, 39619511, 40567171, 40853653, 40949371, 43650223, 48421381, 51381373, 51838333, 53357921, 53878483, 55093697, 56126071, 56885473, 59424821, 60003091, 61021801, 61168031, 63740447, 64129381, 65091797, 65212603, 66061381, 67038133, 68269153, 68888863, 70513213, 73401371, 73433431, 74818633, 74948147, 75467323, 76642021, 76674781, 77463121, 78785981, 78885647, 79284941, 79986131, 85568281, 87517501, 87657571, 88218971, 93027131, 95205041, 95533901, 96119941, 97297397, 97851797, 98333551, 103901533, 104015983, 105701821, 108372811, 109779601, 110880043, 111629897, 112104791, 114494381, 114654583, 120825251, 121030981, 121484203, 122848951, 129573991, 130042921, 130897691, 131583523, 133003711, 133478801, 134518301, 135257053, 136128763, 139245947, 144414733, 146626397, 149906681, 151929163, 152252171, 156904021, 157513903, 157889803, 158784361, 159728731, 161245547, 162578641, 166465993, 166852421, 167626621, 168596891, 169911197, 171279571, 172309453, 178053947, 178203761, 179404541, 181213271, 182222041, 185672803, 187359103, 188590291, 190857941, 193295173, 194963413, 195015661, 195643183, 197268947, 203198731, 204480823, 209053993, 209920481, 210788761, 211604401, 214006031, 219126797, 224196043, 229606651, 231709213, 231937091, 232564333, 235311301, 235368701, 235598371, 236058047, 237382111, 237843523, 238825511, 239519897, 243882647, 247401197, 250530211, 251953591, 253381003, 260759773, 261727397, 270824443, 273788131, 276208003, 278763451, 279451061, 280264783.

Some larger examples :