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centered square n.  and  strong prime

First numbers that belong to both sets:

41, 613, 1301, 1741, 1861, 2381, 2521, 3613, 4513, 7321, 9941, 13613, 14281, 14621, 26681, 38921, 47741, 52813, 54121, 56113, 79601, 94613, 99013, 106261, 110921, 134681, 148513, 167621, 199081, 204161, 237361, 244301, 252761, 255613, 303421, 319201, 332113, 335381, 370661, 377581, 391613, 413141, 459841, 479221, 485113, 501001, 529421, 531481, 552301, 556513, 599513, 632813, 662401, 667013, 718801, 742981, 787513, 800113, 820481, 859361, 864613, 964661, 967441, 987013, 995461, 1006781, 1009621, 1073113, 1078981, 1123501, 1126501, 1147613, 1153681, 1178113, 1326821, 1336613, 1343161, 1379461, 1426361, 1446701, 1460341, 1515541, 1529501, 1720513, 1746581, 1803101, 1833613, 1899301, 2103301, 2161121, 2257813, 2279113, 2287661, 2300513, 2313401, 2422201, 2506561, 2556061, 2619761, 2679613, 2693521, 2716781, 2820313, 2858441, 2892013, 2940313, 3023341, 3077681, 3172681, 3187813, 3223261, 3228341, 3279361, 3330781, 3356641, 3403441, 3429581, 3455821, 3471613, 3498013, 3620741, 3647701, 3674761, 3822613, 3839221, 3917201, 3973381, 4207901, 4277813, 4348301, 4354201, 4395613, 4443181, 4503001, 4593481, 4605613, 4648201, 4678741, 4789513, 4808101, 4864081, 5027621, 5091241, 5123201, 5155261, 5168113, 5252041, 5415341, 5428513, 5514521, 5541121, 5661613, 5776601, 5879021, 5920241, 6072613, 6128501, 6226921, 6376021, 6390313, 6426113, 6498013, 6555821, 6679513, 6716113, 6848701, 6878341, 6922921, 6937813, 7050013, 7163113, 7292381, 7415101, 7469113, 7608901, 7742113, 7757861, 7924181, 7956061, 7980013, 8044061, 8084221, 8124481, 8164841, 8221513, 8319121, 8359961, 8483081, 8698621, 8824201, 8925313, 8993041, 9095113, 9439513, 9509161, 9570313, 9968113, 10401361, 10649113, 10815901, 11002741, 11134481, 11143921, 11324041, 11496013, 11563241, 11572861, 11640313, 11804941, 11863321, 11902321, 12009901, 12029513, 12206741, 12325613, 12545041, 12575113, 12776513, 12806861, 12928613, 12948961, 13081613, 13307641, 13338613, 13650313, 13786501, 13891721, 13944481, 13986761, 14050301, 14391613, 14574601, 14715313, 14802241, 15207613, 15340261, 15518021, 15708013, 15966901, 16102813, 16125521, 16468061, 16617613, 17046961, 17105401, 17117101, 17163941, 17469961, 17731013, 17790613, 18880513, 18905101, 19028281, 19213801, 19350421, 19813513, 19851301, 19939613, 19964881, 20040781, 20282081, 20640313, 20936921, 21118501, 21183541, 21196561, 21418513, 21654781, 21707461, 21813013, 21918821, 21985081, 22038161, 22411513, 22680113, 23018113, 23045261, 23126801, 23317621, 23399641.

Some larger examples :