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centered pentagonal n.  and  prime n.

First numbers that belong to both sets:

31, 181, 331, 601, 1051, 1381, 3331, 4951, 5641, 5881, 9151, 11731, 12781, 14251, 17431, 17851, 19141, 21391, 31081, 33931, 41281, 43891, 51481, 52201, 61231, 63601, 67651, 70141, 70981, 84181, 92641, 100501, 104551, 107641, 116101, 126001, 130531, 133981, 139831, 143401, 174901, 185641, 206641, 224251, 225751, 230281, 244141, 248851, 256801, 261631, 317731, 323101, 324901, 330331, 346891, 375391, 385141, 393031, 415141, 417181, 433681, 459031, 467641, 474151, 485101, 491731, 511891, 520981, 527851, 539401, 546391, 567631, 574801, 603931, 626251, 633781, 636301, 674701, 695641, 763141, 819391, 839551, 874681, 901501, 934831, 937891, 984391, 1009651, 1012831, 1100581, 1127281, 1130641, 1157701, 1212781, 1265581, 1294201, 1326781, 1337731, 1426951, 1461151, 1519051, 1522951, 1618051, 1630141, 1678951, 1699501, 1711891, 1728481, 1761901, 1778731, 1799881, 1829701, 1881391, 1916251, 1920631, 2022751, 2040781, 2077081, 2095351, 2118301, 2150641, 2187901, 2263381, 2301601, 2344981, 2379001, 2403451, 2418181, 2437891, 2462641, 2482531, 2542681, 2583181, 2618881, 2644531, 2706601, 2722231, 2727451, 2769391, 2785201, 2790481, 2806351, 2897131, 3000301, 3049801, 3178141, 3229081, 3251851, 3337951, 3384331, 3454501, 3460381, 3478051, 3507601, 3525391, 3531331, 3597001, 3621031, 3693601, 3724051, 3766891, 3797641, 3915631, 3946981, 3972151, 4041781, 4176391, 4195801, 4221751, 4273891, 4300081, 4359301, 4412281, 4438891, 4573141, 4600231, 4620601, 4681981, 4736881, 4757551, 4785181, 4819831, 4924531, 4987891, 5016181, 5101531, 5122981, 5274391, 5354581, 5442751, 5539081, 5651281, 5810251, 5871391, 5894401, 5902081, 5925151, 5986891, 5994631, 6056731, 6205501, 6244951, 6460141, 6492331, 6654481, 6662641, 6728101, 6859981, 6951391, 7026631, 7127581, 7288891, 7391701, 7460641, 7573351, 7599481, 7643131, 7783651, 7810141, 7889881, 7916551, 7961101, 8203831, 8212891, 8285551, 8322001, 8431831, 8505451, 8533141, 8653651, 8840701, 8868931, 8953891, 9297781, 9413851, 9648151, 9835681, 9915181, 10035031, 10045051, 10125391, 10155601, 10165681, 10398901, 10490881, 10562701, 10686391, 10988281, 11030251, 11188351, 11273131, 11315641, 11497201, 11540131, 11658601, 12061531, 12182641, 12226831, 12899281, 12956131, 13127431, 13138891, 13450201, 13788631, 13870951, 14119381, 14502181, 14586601, 14647051, 14683381, 14792641, 14975641, 15122851, 15172081, 15531391, 15681301, 15731431, 15920131, 16021231, 16071901.

Some larger examples :