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junction n.  and  weak prime

First numbers that belong to both sets:

103, 109, 113, 313, 317, 509, 709, 911, 919, 1013, 1217, 1409, 1609, 1613, 1621, 1811, 2017, 2113, 2311, 2713, 2719, 2917, 2927, 3209, 3221, 3413, 3617, 3623, 3823, 4021, 4027, 4111, 4519, 4523, 4723, 4919, 5011, 5209, 5419, 5813, 5827, 6121, 6719, 6917, 7019, 7213, 7219, 7417, 7621, 7829, 8123, 8317, 8527, 8719, 8933, 9013, 9227, 9421, 9623, 9631, 9817, 9833, 10009, 10613, 11119, 11321, 11719, 11927, 12011, 12211, 12413, 12421, 12613, 12619, 12823, 13109, 13313, 13523, 13711, 13723, 13913, 13921, 14011, 14207, 14221, 14411, 14423, 15017, 15031, 15107, 15319, 15511, 15923, 16007, 16421, 16831, 17029, 17033, 17123, 17321, 17519, 17923, 17929, 18013, 18413, 19319, 19717, 19727, 19919, 19927, 20023, 20117, 20509, 20719, 21013, 21407, 21419, 21613, 21617, 21821, 22111, 22307, 22511, 22721, 22727, 22921, 23209, 23819, 24023, 24029, 24109, 24113, 24121, 24517, 24919, 24923, 25411, 25423, 25819, 26021, 26029, 26113, 26119, 26321, 26513, 26717, 26731, 26927, 27017, 27211, 27617, 27631, 27827, 28031, 28111, 28123, 28319, 28517, 28729, 28933, 29023, 29429, 29633, 30013, 30029, 30211, 30817, 31019, 31321, 31513, 31517, 31723, 32009, 32213, 32413, 32611, 32621, 33029, 33119, 33317, 33721, 34213, 34217, 34613, 34819, 35027, 35111, 35117, 35327, 35731, 35933, 36013, 36017, 36217, 36833, 37021, 37123, 37313, 37321, 37517, 37717, 38011, 39023, 39119, 39317, 39323, 39521, 39733, 39937, 41413, 41611, 41621, 41627, 41813, 42019, 42023, 42727, 42929, 43019, 43411, 43613, 44021, 44029, 44123, 44917, 44927, 45013, 45413, 45823, 45827, 45833, 46027, 46523, 46727, 46933, 47017, 47221, 47419, 47629, 47819, 48029, 48121, 48527, 48733, 49019, 49223, 49417, 49433, 49831, 50023, 50033, 50423, 51521, 51721, 52817, 53117, 53327, 53527, 53719, 53731, 53927, 54013, 54217, 54413, 54421, 54631, 54833, 55021, 55117, 55127, 55721, 55733, 55933, 56633, 56827, 57331, 57529, 57719, 57731, 57923.

Some larger examples :