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centered square n.  and  unprimeable n.

First numbers that belong to both sets:

3785, 5725, 9385, 10805, 13285, 13945, 18625, 20605, 21425, 22685, 24865, 35645, 37265, 38365, 40045, 45905, 50245, 53465, 58825, 69565, 73345, 77225, 82825, 85285, 86945, 89465, 93745, 104425, 116645, 126505, 144185, 147425, 155125, 160745, 164165, 166465, 181805, 184225, 190345, 206725, 209305, 222445, 229165, 233245, 235985, 240125, 242905, 247105, 254185, 257045, 261365, 271585, 276025, 286525, 298765, 309685, 330485, 333745, 372385, 384565, 411325, 416785, 420445, 425965, 448405, 457925, 463685, 473365, 477265, 483145, 487085, 497005, 517145, 527365, 537685, 548105, 554405, 586445, 590785, 597325, 601705, 619385, 623845, 630565, 635065, 646385, 653225, 664705, 680945, 699745, 704485, 716405, 752765, 765085, 772525, 777505, 815365, 823045, 828185, 861985, 867245, 875165, 880465, 893785, 901825, 907205, 961885, 970225, 984205, 1018165, 1026745, 1032485, 1046905, 1061425, 1076045, 1084865, 1135525, 1159765, 1175045, 1221485, 1227745, 1243465, 1268825, 1284805, 1300885, 1323565, 1333345, 1339885, 1349725, 1356305, 1366205, 1382785, 1389445, 1416245, 1422985, 1491265, 1501645, 1519025, 1526005, 1536505, 1543525, 1561145, 1578865, 1589545, 1596685, 1607425, 1614605, 1625405, 1643485, 1668965, 1679945, 1698325, 1705705, 1716805, 1735385, 1761565, 1772845, 1791725, 1818325, 1829785, 1837445, 1848965, 1856665, 1868245, 1887625, 1895405, 1926685, 1934545, 1954265, 1966145, 1974085, 1994005, 2034145, 2046265, 2086925, 2127985, 2156965, 2211305, 2219725, 2232385, 2240845, 2253565, 2283385, 2296225, 2317705, 2360965, 2369665, 2391485, 2404625, 2413405, 2435425, 2457545, 2470865, 2524505, 2538005, 2583265, 2628925, 2638105, 2651905, 2661125, 2684245, 2698165, 2707465, 2744825, 2768305, 2791885, 2815565, 2848885, 2872805, 2896825, 2911285, 2959745, 2984125, 3008605, 3057865, 3067765, 3107525, 3132505, 3142525, 3167645, 3192865, 3218185, 3233425, 3243605, 3258905, 3269125, 3320465, 3346285, 3372205, 3413885, 3424345, 3440065, 3492725, 3529825, 3609985, 3626125, 3653105, 3680185, 3718265, 3734645, 3762025, 3773005, 3789505, 3817085, 3828145, 3844765, 3855865, 3883685, 3900425, 3911605, 3928405, 3939625, 3956485, 3984665, 3995965, 4041325, 4184725, 4213705, 4225325, 4312985, 4360105, 4371925, 4389685, 4401545, 4449145, 4461085, 4509005, 4521025, 4551145, 4569265, 4581365, 4599545, 4642105, 4660405, 4703245, 4764785, 4814305, 4857845, 4876565, 4907845.

Some larger examples :