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de Polignac n.  and  triangular n.

First numbers that belong to both sets:

1, 46971, 79003, 93961, 166753, 203203, 224785, 286903, 334153, 542361, 765703, 901153, 905185, 983503, 1181953, 1553203, 1771903, 1886653, 1915903, 2053351, 2252503, 2284453, 2934253, 3081403, 3232153, 3270403, 3837835, 3913003, 3915801, 4014361, 4255903, 4937653, 5253661, 5361175, 5519503, 5569453, 5925403, 6402831, 6543153, 6747301, 6835753, 6924781, 7834861, 8134561, 8464555, 8476903, 8576011, 9446031, 9493903, 9867903, 10024003, 10776403, 11037951, 12273535, 12814453, 13181545, 13883815, 14180475, 14701753, 15045355, 15710815, 15761305, 16117003, 16168141, 16459453, 16718653, 16927471, 17751861, 18589753, 18982041, 19179721, 20081953, 20464003, 21141253, 21160765, 21474181, 21533203, 22028203, 22428253, 23239153, 23546953, 23711941, 24147775, 24293935, 24904153, 26082253, 26140065, 26190703, 26539255, 27132661, 27280191, 27509653, 27844453, 29203903, 30689695, 31066903, 31660903, 32140153, 32501953, 32784753, 33109453, 33476653, 33895261, 34590403, 35091253, 35225421, 35326215, 35595703, 36487153, 37311841, 38250631, 38276875, 40163203, 40297753, 40702753, 41929903, 42490371, 43594453, 45864253, 46672291, 47458153, 47604403, 48073915, 48871441, 51638203, 52372495, 53649261, 54262153, 54889003, 55361503, 55994653, 56535661, 57015181, 58725703, 59214403, 62524153, 63365653, 63873253, 64235445, 65236753, 66096253, 66372481, 70122403, 70870465, 71156485, 71490903, 71538741, 73174753, 74450503, 77109571, 80422903, 80625951, 80765695, 81223885, 81581151, 82721953, 82876375, 84584521, 84779731, 87615703, 89171335, 89211403, 90296641, 90821503, 90942841, 91631953, 92827125, 94139781, 94703203, 94868425, 95199301, 95530753, 95738203, 98035003, 98245153, 99934453.