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de Polignac n.  and  frugal n.

First numbers that belong to both sets:

14375, 26875, 27097, 43687, 88837, 96721, 103243, 103259, 104875, 105149, 110125, 112627, 119021, 121801, 122317, 123883, 129107, 129997, 137677, 149683, 158171, 164561, 180989, 182351, 184877, 188125, 192721, 197213, 205057, 205379, 206143, 206875, 211631, 226981, 231093, 233227, 234269, 242271, 242501, 243187, 259375, 269375, 271633, 271663, 272473, 272861, 293077, 304927, 307501, 309809, 315217, 322373, 326041, 330773, 338125, 339913, 348823, 356875, 360937, 365117, 367993, 368219, 378359, 389017, 399521, 404587, 409375, 410881, 429779, 441007, 443111, 450179, 459999, 476561, 489119, 490617, 540625, 555131, 573839, 584647, 591875, 595625, 600943, 645869, 668039, 683929, 703423, 709375, 737107, 746711, 757687, 786769, 822649, 840625, 852607, 888191, 953197, 971875, 978125, 980947, 1000309, 1011875, 1012499, 1012817, 1017283, 1017839, 1025999, 1027625, 1028863, 1032875, 1035423, 1035875, 1045601, 1049375, 1052081, 1054915, 1056757, 1057949, 1060807, 1066873, 1076677, 1080643, 1089125, 1091909, 1092701, 1104299, 1107371, 1108375, 1110259, 1110753, 1115375, 1117151, 1119371, 1126409, 1131313, 1136375, 1136441, 1140625, 1141847, 1142467, 1148021, 1152457, 1156393, 1164485, 1167229, 1173097, 1177417, 1180199, 1181875, 1182875, 1183375, 1188125, 1192375, 1199227, 1200157, 1202375, 1208323, 1208639, 1208827, 1214563, 1223729, 1227761, 1233163, 1237625, 1241125, 1245861, 1247159, 1251397, 1257373, 1259839, 1266875, 1268443, 1272187, 1272517, 1273597, 1281013, 1283713, 1291123, 1293125, 1296149, 1298413, 1300567, 1309499, 1309859, 1319021, 1323823, 1325783, 1331875, 1335839, 1343281, 1351619, 1353821, 1356029, 1360901, 1364941, 1366411, 1366855, 1367983, 1371791, 1373743, 1374401, 1377763, 1378123, 1378213, 1383463, 1387933, 1390041, 1391743, 1396079, 1396357, 1417691, 1426537, 1426603, 1438199, 1440943, 1447117, 1452217, 1455731, 1459375, 1461523, 1461943, 1466991, 1474237, 1474685, 1476133, 1478741, 1485625, 1488277, 1493125, 1494341, 1496045, 1496875, 1500259, 1507273, 1508171, 1508291, 1510625, 1512911, 1518029, 1518127, 1521889, 1524667, 1525321, 1527209, 1527667, 1530169, 1531391, 1542083, 1545209, 1545723, 1550017, 1560307, 1566541, 1568683, 1575097, 1582259, 1585183, 1588271, 1590817, 1601707, 1603643, 1606087, 1611071, 1611875, 1625527, 1632251, 1638485, 1645451, 1646471, 1647277, 1651483, 1659933, 1660183, 1664531, 1664617, 1669375, 1670729, 1675957, 1677043, 1677613.

Some larger examples :