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junction n.  and  Sophie Germain prime

First numbers that belong to both sets:

113, 509, 719, 911, 1013, 1409, 1811, 3413, 3623, 3821, 4019, 4919, 6113, 6323, 6521, 7211, 7823, 8111, 8513, 9221, 9419, 9629, 10613, 11321, 11519, 12011, 12821, 13313, 13913, 14009, 14621, 15923, 16421, 16823, 19319, 19919, 20921, 21011, 21221, 21419, 21611, 23819, 26111, 29021, 31019, 31319, 31721, 32009, 33023, 33119, 33521, 33713, 35111, 35933, 36629, 36821, 39521, 41621, 42023, 42719, 42923, 43013, 44111, 44729, 46523, 48029, 48731, 49433, 50021, 50411, 50423, 51521, 54011, 54413, 55721, 55733, 55931, 57329, 58013, 59123, 59723, 60719, 63419, 65633, 66029, 67433, 69029, 69431, 73523, 74219, 75329, 76421, 78233, 78623, 78839, 81629, 82529, 82721, 83423, 84533, 85223, 85829, 87221, 90011, 90833, 91121, 91529, 93113, 93323, 94229, 94421, 95723, 97523, 97931, 98639, 99041, 100811, 101921, 102611, 103319, 105929, 106019, 107021, 108011, 108821, 109313, 109919, 111623, 112919, 113213, 119429, 122819, 123719, 123923, 124823, 125921, 127733, 128819, 133013, 135221, 136523, 138923, 140813, 142211, 142223, 145121, 145721, 146213, 146819, 147029, 148013, 148829, 149333, 149531, 150323, 152111, 155219, 158129, 159233, 159431, 159629, 159839, 160019, 160031, 160619, 161033, 161123, 162419, 162821, 164621, 164831, 166823, 167729, 168029, 169733, 171023, 173021, 173219, 175229, 176933, 177839, 179429, 179633, 180413, 181523, 183119, 184631, 184823, 184829, 185123, 185723, 186419, 189041, 189929, 190523, 192113, 194723, 194933, 196331, 196739, 198323, 201011, 201209, 204311, 204521, 206033, 206933, 207821, 208121, 208931, 209021, 209213, 210209, 211313, 213929, 215723, 217121, 218213, 219731, 220019, 220721, 220919, 221219, 221411, 221621, 222023, 222311, 222713, 224033, 224729, 228023, 228521, 230819, 233021, 236429, 237929, 238019, 243011, 243623, 244313, 246329, 246731, 246929, 247421, 249233, 250829, 251519, 253919, 255023, 257123, 257321, 260723, 262121, 262733, 263429, 265619, 267419, 268133, 274019, 275531, 276833, 277331, 279941, 280121, 283631, 284723, 285023, 285839, 287219, 288731, 289031, 290039, 290429, 291113, 292223, 293729, 298631, 300413, 300623, 301319.

Some larger examples :