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a-pointer prime  and  alternating n.

First numbers that belong to both sets:

101, 103, 181, 701, 2143, 2521, 6121, 6301, 8101, 8543, 1010501, 1010903, 1012307, 1012703, 1012903, 1016123, 1016341, 1030723, 1034147, 1034323, 1034707, 1036163, 1036921, 1038503, 1038563, 1050169, 1054549, 1056521, 1056541, 1070149, 1070323, 1074581, 1076303, 1090129, 1092107, 1092929, 1094161, 1094183, 1096163, 1216507, 1218787, 1230301, 1236583, 1238921, 1250983, 1252129, 1252921, 1254301, 1254503, 1256303, 1274183, 1276543, 1290109, 1292387, 1296109, 1296343, 1296523, 1410781, 1414921, 1432703, 1434109, 1438181, 1452301, 1454149, 1456187, 1474523, 1478129, 1492541, 1494161, 1610107, 1612141, 1616723, 1618741, 1650301, 1652543, 1654127, 1674107, 1692589, 1814543, 1816121, 1836763, 1854529, 1872503, 1894181, 1898921, 3010981, 3012101, 3012187, 3012323, 3018121, 3030127, 3030163, 3034189, 3036167, 3038363, 3058361, 3058729, 3070187, 3070321, 3072169, 3078109, 3090161, 3094501, 3096323, 3212723, 3214109, 3218123, 3238309, 3258301, 3258323, 3272147, 3272387, 3272747, 3290983, 3294143, 3298543, 3410347, 3410941, 3414349, 3430547, 3432721, 3458783, 3472549, 3476783, 3610303, 3610781, 3612121, 3618709, 3618761, 3632903, 3638521, 3652903, 3654503, 3658943, 3694147, 3810589, 3812923, 3814903, 3816107, 3816941, 3876109, 3878143, 3892123, 5014381, 5016901, 5032961, 5034301, 5034521, 5036147, 5036543, 5038321, 5050189, 5050327, 5052301, 5052787, 5054743, 5058143, 5058761, 5074103, 5096347, 5214103, 5230109, 5230327, 5250503, 5254169, 5258503, 5270501, 5274967, 5276303, 5292769, 5410309, 5410703, 5412581, 5416949, 5432983, 5452103, 5452747, 5458121, 5470187, 5470909, 5612149, 5618149, 5618323, 5630507, 5632541, 5652583, 5652727, 5690501, 5690561, 5812523, 5814167, 5816521, 5830343, 5832361, 5852501, 5854141, 5892989, 5894723, 5898367, 7010581, 7012507, 7014583, 7014769, 7014947, 7016101, 7016341, 7018321, 7034723, 7036741, 7056349, 7074101, 7074569, 7090549, 7210781, 7212943, 7214303, 7218503, 7218721, 7232341, 7234361, 7234781, 7236503, 7250161, 7250363, 7254349, 7258709, 7290721, 7296127, 7296301, 7296983, 7410307, 7410383, 7410527, 7412507, 7418507, 7430947, 7432543, 7434143, 7434523, 7434949, 7450721, 7470989, 7610749, 7612127, 7616923, 7634161, 7652321, 7672943, 7676743, 7810301, 7818761, 7830323, 7830521, 7836107, 7870327, 7894921, 9016921, 9018941, 9030143, 9036509, 9052181, 9054109, 9078781, 9096743, 9214703, 9216107, 9236141, 9236503, 9250361, 9252521, 9276121, 9290101, 9290947, 9414949, 9478387, 9492349, 9492563, 9494783, 9612721, 9632729.

Some larger examples :