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aban n.  and  Sophie Germain prime

First numbers that belong to both sets:

2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1000151, 1000193, 1000211, 1000403, 1000589, 2000039, 2000261, 2000573, 2000699, 2000903, 2000969, 3000251, 3000671, 3000953, 4000043, 4000169, 4000439, 4000523, 4000553, 4000589, 4000673, 4000679, 4000823, 4000889, 4000949, 5000111, 5000321, 5000381, 5000399, 5000741, 5000783, 5000903, 5000981, 6000119, 6000191, 6000233, 6000479, 6000569, 6000581, 6000653, 6000773, 6000899, 7000313, 7000589, 7000739, 8000231, 8000579, 8000651, 8000831, 9000203, 9000269, 9000473, 9000683, 10000079, 10000121, 10000169, 10000253, 10000271, 10000439, 11000189, 11000393, 11000603, 11000651, 11000849, 12000899, 13000049, 13000133, 13000139, 13000913, 13000973, 14000183, 14000963, 15000413, 15000533, 16000511, 16000769, 17000129, 17000339, 17000891, 17000999, 18000089, 18000149, 18000539, 18000683, 18000803, 19000409, 19000511, 19000571, 19000673, 19000853, 19000973, 20000243, 20000693, 20000723, 20000801, 20000969, 21000191, 21000251, 21000461, 21000599, 22000001, 22000103, 22000409, 22000493, 22000553, 22000619, 22000859, 23000123, 23000699, 23000723, 23000909, 23000921, 24000083, 24000131, 24000233, 25000373, 25000649, 25000691, 25000841, 26000003, 26000069, 26000099, 26000231, 26000291, 27000089, 27000191, 27000299, 27000563, 27000761, 28000019, 28000061, 28000421, 28000463, 28000541, 28000733, 28000961, 29000879, 30000023, 30000293, 30000611, 30000683, 30000749, 31000241, 31000433, 31000499, 31000559, 31000793, 31000829, 31000841, 32000651, 32000669, 32000753, 33000431, 33000563, 33000959, 34000019, 34000643, 34000679, 34000913, 34000979, 35000159, 35000321, 35000681, 35000741, 35000879, 36000323, 36000599, 37000181, 37000193, 37000811, 37000973, 38000069, 38000129, 38000663, 38000849, 38000981, 39000173, 39000233, 39000281, 39000509, 39000569, 39000653, 39000971, 40000223, 40000241, 40000349, 40000721, 41000159, 41000483, 41000681, 41000759, 41000783, 41000819, 42000011, 42000683, 42000779, 43000151, 43000169, 43000241, 43000319, 43000343, 43000679, 43000799, 44000009, 44000321, 44000783, 45000149, 45000239, 45000629, 46000511, 46000763, 47000171, 47000183, 47000381, 47000819, 48000041, 48000131, 48000209, 48000509, 48000779, 48000941, 48000971, 49000109, 49000313, 49000331, 50000063, 50000231, 50000399, 50000921, 51000359, 51000413, 51000479, 51000923, 52000043, 52000061, 52000313, 52000583, 52000673, 52000709, 52000829, 52000901, 53000141, 53000693.

Some larger examples :