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centered pentagonal n.  and  weak prime

First numbers that belong to both sets:

31, 181, 601, 1051, 1381, 3331, 5641, 5881, 14251, 19141, 31081, 41281, 43891, 51481, 52201, 61231, 63601, 67651, 70141, 70981, 84181, 92641, 100501, 104551, 116101, 130531, 133981, 206641, 225751, 230281, 256801, 317731, 323101, 324901, 330331, 385141, 393031, 433681, 459031, 467641, 474151, 520981, 527851, 539401, 546391, 574801, 674701, 695641, 819391, 874681, 901501, 937891, 1009651, 1012831, 1130641, 1157701, 1265581, 1294201, 1337731, 1426951, 1461151, 1519051, 1522951, 1618051, 1630141, 1699501, 1711891, 1728481, 1778731, 1829701, 1881391, 1916251, 2022751, 2077081, 2095351, 2118301, 2150641, 2263381, 2301601, 2418181, 2437891, 2462641, 2542681, 2583181, 2618881, 2706601, 2727451, 2769391, 2790481, 2897131, 3000301, 3178141, 3337951, 3384331, 3507601, 3525391, 3531331, 3724051, 3915631, 3972151, 4273891, 4300081, 4412281, 4573141, 4681981, 4757551, 4819831, 4987891, 5101531, 5354581, 5442751, 5539081, 5651281, 5894401, 5925151, 5986891, 6056731, 6492331, 6662641, 6728101, 6859981, 6951391, 7026631, 7288891, 7391701, 7783651, 7810141, 7889881, 7916551, 7961101, 8285551, 8322001, 8431831, 8533141, 8840701, 9413851, 9648151, 9915181, 10035031, 10045051, 10125391, 10155601, 10398901, 10562701, 10988281, 11540131, 11658601, 12182641, 12226831, 12899281, 13138891, 13788631, 13870951, 14119381, 14586601, 14647051, 14683381, 15531391, 15681301, 15920131, 16224391, 16339231, 16492981, 16686181, 16789681, 17272531, 17430601, 17576131, 17589391, 17788891, 17855641, 17895751, 18394141, 18762151, 18885631, 18995731, 19551031, 19705141, 19761331, 20001031, 20100151, 20171101, 20270641, 20398981, 20685631, 21075781, 21250351, 21264931, 21425641, 21793141, 22134001, 22372681, 22492501, 23096401, 23172451, 23401351, 23462581, 23831641, 24094801, 24281431, 24328201, 24845641, 25098481, 25528051, 26381881, 26773141, 26822251, 27084931, 28232401, 28637101, 28840531, 29027641, 29044681, 29232451, 29249551, 29437981, 29455141, 29592601, 29920351, 30493891, 31532881, 31906891, 31978381, 32175391, 32193331, 32463031, 33699781, 33773251, 33920431, 35711551, 35730451, 35938681, 37162201, 37626301, 37723351, 37859431, 37956781, 38249581, 38484631, 39511501, 39930031, 40230331, 40411051, 40652641, 40814101, 41137981, 41850931, 42281641, 42363931, 42528751, 42673231, 43336831, 43670551, 43775101, 44426101, 45124381, 46063891, 46407931, 46645201, 46839781, 47099851, 47884381, 47950051, 48213181, 49006891, 49807081, 50097631, 50164801, 50344141, 50546281, 50974351, 51449581, 51722131, 52269391, 53372551, 53835601, 53998141, 54674131, 54837931, 55519141.

Some larger examples :