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centered square n.  and  weak prime

First numbers that belong to both sets:

13, 61, 113, 181, 313, 421, 761, 1013, 1201, 2113, 3121, 5101, 8581, 9661, 10513, 12641, 16381, 19013, 19801, 21013, 21841, 23981, 24421, 30013, 34061, 36721, 37813, 41761, 44701, 49613, 51521, 59513, 60901, 68821, 70313, 71821, 76441, 82013, 83641, 86113, 90313, 97241, 100801, 101701, 105341, 135721, 139921, 143113, 161881, 163021, 165313, 168781, 177013, 185441, 205441, 210601, 218461, 223781, 234613, 241513, 273061, 277513, 282001, 304981, 312841, 337021, 365513, 382813, 388081, 405901, 424121, 427813, 431521, 437113, 450301, 452201, 456013, 481181, 489061, 491041, 511061, 525313, 539761, 571381, 584281, 595141, 603901, 617161, 637321, 673961, 685621, 695021, 697381, 702113, 726013, 750313, 770041, 782501, 825613, 843701, 883121, 904513, 909901, 923441, 926161, 1064341, 1108561, 1117513, 1156721, 1171981, 1187341, 1193513, 1230881, 1262461, 1278401, 1288013, 1304113, 1429741, 1453513, 1470613, 1557613, 1568221, 1629013, 1639861, 1676281, 1702013, 1727941, 1757813, 1806901, 1872113, 2002001, 2018041, 2042221, 2070613, 2111513, 2132113, 2186141, 2330641, 2334961, 2343613, 2356621, 2365313, 2417801, 2542513, 2574181, 2578721, 2601481, 2610613, 2740141, 2758901, 2763601, 2829821, 2834581, 2853661, 3137513, 3238513, 3248701, 3289613, 3341113, 3351461, 3377401, 3408661, 3535141, 3540461, 3567121, 3593881, 3658513, 3696481, 3723721, 3729181, 3795013, 3878113, 3889261, 3934013, 3962113, 3979021, 4007281, 4035641, 4047013, 4058401, 4121321, 4173161, 4190513, 4219513, 4307113, 4545113, 4636013, 4715521, 4727813, 4832941, 4901581, 4945513, 4989641, 5104013, 5136013, 5232613, 5278001, 5317061, 5494613, 5581141, 5749441, 5763013, 5844781, 5885881, 5982341, 6003113, 6093541, 6107513, 6121501, 6191681, 6262261, 6368881, 6752813, 6804361, 6811741, 6863513, 6900613, 7035001, 7065041, 7178261, 7315313, 7353613, 7407401, 7445941, 7546613, 7640141, 7679281, 7805201, 7836841, 8116421, 8197201, 8262113, 8302813, 8343613, 8491321, 8590513, 8757113, 8773861, 8815801, 8857841, 8908421, 8950681, 9197761, 9240701, 9249301, 9309613, 9456901, 9465601, 9500441, 9552821, 9834613, 9852361, 9879013, 9941341, 10030721, 10057613, 10102513, 10174561, 10264981, 10511113, 10529461, 10621441, 10741613, 10760161, 10862461, 10899781, 10993361, 11087341, 11381221, 11515201, 11524801, 11834113, 11931613, 12246301, 12395221, 12495001, 12605221, 12625313, 12655481, 12705841.

Some larger examples :