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de Polignac n.  and  square n.

First numbers that belong to both sets:

1, 40401, 62001, 96721, 121801, 192721, 326041, 410881, 555025, 660969, 683929, 772641, 786769, 822649, 1343281, 1390041, 1530169, 1739761, 1885129, 1923769, 1962801, 2283121, 2544025, 2913849, 3207681, 3214849, 3352561, 3396649, 3613801, 3775249, 3853369, 4060225, 4289041, 4338889, 4397409, 4490161, 4756761, 4800481, 4879681, 5058001, 5175625, 5527201, 5736025, 5745609, 5851561, 6295081, 6487209, 6548481, 7017201, 7155625, 7230721, 7241481, 7252249, 7789681, 8003241, 8173881, 8185321, 8323225, 8334769, 9126441, 9603801, 9840769, 10182481, 10400625, 10543009, 10804369, 10896601, 11108889, 11363641, 11785489, 12159169, 12313081, 12766329, 14010049, 14478025, 14538969, 15077689, 15531481, 17480761, 19193161, 19439281, 19651489, 20493729, 20729809, 20912329, 22212369, 22439169, 22553001, 22648081, 22953681, 23011209, 24039409, 24117921, 24235929, 24453025, 24730729, 25010001, 25090081, 25371369, 25411681, 25816561, 25999801, 27615025, 27825625, 28804689, 28976689, 29452329, 29560969, 30283009, 30415225, 30680521, 31775769, 32001649, 32364721, 32433025, 32638369, 32844361, 32959081, 33466225, 33744481, 34140649, 34234201, 34468641, 34869025, 35414401, 35772361, 36180225, 36397089, 36469521, 36566209, 36784225, 37027225, 37491129, 39955041, 40564161, 40998409, 41254929, 41589601, 41770369, 42601729, 43151761, 44555625, 44635761, 45576001, 45846441, 47018449, 47210641, 47265625, 47844889, 48233025, 48539089, 48762289, 49463089, 49632025, 50537881, 50822641, 51912025, 51998521, 52171729, 52345225, 54243225, 54656449, 55398249, 55487601, 55845729, 55875625, 56115081, 56385081, 56505289, 57562569, 57714409, 57927321, 58415449, 58599025, 59706529, 60512841, 60855601, 61074225, 61512649, 61732449, 62932489, 63409369, 63984001, 65399569, 67354849, 67617729, 68873401, 69872881, 70509609, 72131049, 72199009, 73017025, 73359225, 73599241, 73805281, 73942801, 74218225, 74701449, 76300225, 76440049, 76895361, 77105961, 77211369, 77246521, 77457601, 78872161, 79085449, 79762761, 80192025, 81234169, 81270225, 81956809, 83046769, 83557881, 84070561, 84143929, 84695209, 85211361, 85359121, 85470025, 85618009, 85655025, 87665769, 88604569, 88981489, 89775625, 91107025, 91145209, 91374481, 96766569, 99620361.