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de Polignac n.  and  unprimeable n.

First numbers that belong to both sets:

3505, 3665, 4195, 4855, 5125, 5755, 6535, 7405, 8915, 9115, 10235, 11015, 11105, 11335, 12595, 13285, 13735, 14375, 14585, 14605, 14975, 16025, 16165, 16405, 16865, 17305, 18155, 18565, 18685, 18845, 19345, 20195, 23725, 23935, 24665, 25295, 25925, 26065, 26615, 26675, 27385, 27575, 28135, 29495, 30415, 30955, 31025, 32225, 33685, 34525, 35305, 35485, 35645, 35715, 38105, 39065, 40105, 40745, 40985, 41425, 42095, 43145, 43565, 45935, 46285, 46425, 46985, 47345, 48005, 48085, 48715, 48745, 48965, 49585, 51275, 51395, 52415, 52475, 53365, 54685, 57215, 58865, 59815, 59935, 60055, 60565, 60785, 61105, 62105, 62395, 62845, 63085, 63935, 64115, 65315, 66775, 66835, 67015, 68065, 68125, 68755, 69085, 70775, 71575, 71755, 72325, 72455, 73495, 73795, 74245, 74915, 76025, 76585, 76925, 77885, 78115, 78385, 79445, 79505, 79895, 80045, 80375, 84155, 85325, 85955, 86335, 87455, 89195, 90665, 92605, 92815, 93125, 93515, 93725, 93745, 93865, 94985, 96205, 96965, 97535, 98275, 98765, 99295, 100285, 100585, 101495, 102865, 104465, 107045, 107395, 107405, 108655, 110405, 110665, 111385, 111395, 111715, 112415, 112495, 114305, 116315, 117095, 118315, 118335, 118645, 118825, 119285, 119465, 119905, 119935, 120115, 121475, 122435, 122585, 123335, 123565, 123575, 124035, 124205, 124385, 124865, 125875, 126085, 126725, 126805, 126905, 127015, 127465, 127895, 129235, 129665, 129875, 131525, 131825, 131885, 133505, 134765, 135125, 138035, 138065, 138475, 138875, 139015, 139285, 140105, 140375, 140785, 141565, 141985, 142475, 142645, 142685, 142745, 143315, 143425, 143455, 143915, 144215, 146105, 146395, 146695, 146825, 147125, 147715, 147845, 147905, 147925, 149465, 150175, 150875, 151315, 152485, 153305, 153805, 154235, 154775, 156095, 157025, 158095, 158915, 159035, 159125, 159245, 160465, 160475, 161195, 161435, 161555, 161695, 162185, 162215, 163205, 163655, 163795, 164285, 164525, 165125, 165145, 165425, 165505, 166135, 166265, 166505, 166715, 166775, 168725, 168875, 168955, 169295, 169865, 170075, 170585, 172015, 172765, 172925, 172955, 173455, 174115, 174715, 175025.

Some larger examples :