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aban n.  and  weak prime

First numbers that belong to both sets:

3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401, 409, 421, 433, 443, 449, 463, 467, 491, 503, 509, 523, 547, 571, 577, 601, 619, 643, 647, 661, 677, 683, 691, 709, 743, 761, 773, 797, 811, 823, 829, 839, 859, 863, 883, 887, 911, 919, 941, 953, 971, 983, 997, 1000003, 1000039, 1000121, 1000133, 1000159, 1000187, 1000199, 1000213, 1000253, 1000291, 1000313, 1000333, 1000367, 1000397, 1000409, 1000429, 1000457, 1000541, 1000547, 1000579, 1000589, 1000621, 1000651, 1000669, 1000679, 1000697, 1000723, 1000777, 1000793, 1000849, 1000861, 1000921, 1000931, 1000973, 1000981, 2000003, 2000039, 2000083, 2000093, 2000113, 2000147, 2000153, 2000177, 2000227, 2000269, 2000293, 2000309, 2000329, 2000353, 2000389, 2000393, 2000417, 2000429, 2000447, 2000503, 2000521, 2000539, 2000597, 2000633, 2000639, 2000659, 2000671, 2000693, 2000699, 2000731, 2000767, 2000813, 2000941, 2000963, 2000969, 2000989, 3000029, 3000077, 3000089, 3000103, 3000133, 3000199, 3000229, 3000251, 3000301, 3000343, 3000359, 3000379, 3000409, 3000469, 3000479, 3000541, 3000553, 3000611, 3000617, 3000643, 3000677, 3000743, 3000761, 3000797, 3000821, 3000869, 3000887, 3000931, 3000953, 3000967, 3000983, 4000039, 4000043, 4000067, 4000081, 4000093, 4000159, 4000169, 4000189, 4000277, 4000303, 4000309, 4000361, 4000379, 4000523, 4000543, 4000573, 4000589, 4000651, 4000673, 4000679, 4000693, 4000723, 4000751, 4000823, 4000861, 4000883, 4000889, 4000901, 4000907, 4000939, 4000951, 4000957, 4000993, 5000011, 5000081, 5000087, 5000113, 5000167, 5000201, 5000213, 5000263, 5000321, 5000339, 5000389, 5000399, 5000423, 5000503, 5000519, 5000543, 5000551, 5000563, 5000581, 5000627, 5000657, 5000689, 5000713, 5000747, 5000761, 5000783, 5000797, 5000861, 5000881, 5000929, 5000939, 5000981, 5000993, 6000023, 6000053, 6000061, 6000073, 6000103, 6000109, 6000121, 6000157, 6000173, 6000199, 6000233, 6000283, 6000307, 6000317, 6000343, 6000377, 6000389, 6000403, 6000431, 6000481, 6000503, 6000557, 6000571, 6000581, 6000619, 6000653, 6000703, 6000733, 6000809, 6000823, 6000829, 6000859, 6000893.

Some larger examples :