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inconsummate n.  and  twin primes

First numbers that belong to both sets:

431, 461, 521, 821, 827, 1049, 1481, 1487, 1871, 1931, 2591, 3251, 3257, 3329, 3371, 3581, 3767, 3821, 4049, 4091, 4127, 4157, 4219, 4241, 4271, 4273, 4649, 4931, 4967, 5231, 5477, 5639, 5881, 6551, 6659, 7331, 7487, 8231, 8597, 8819, 8837, 9041, 9341, 9419, 9437, 10037, 10331, 10937, 11057, 11491, 11549, 11777, 12041, 12107, 13217, 13709, 13997, 14321, 14387, 14591, 14627, 14867, 15137, 15641, 15737, 15887, 17027, 17207, 17387, 17657, 17681, 17921, 17987, 18131, 18251, 18287, 19181, 20147, 20357, 20477, 20507, 20717, 20807, 20981, 21017, 21059, 21317, 21587, 21611, 21737, 22037, 22271, 22481, 23537, 23627, 23687, 24917, 25031, 25307, 25577, 25847, 25931, 26111, 26951, 27281, 28097, 28109, 28181, 28277, 28307, 28547, 28661, 28751, 29021, 29207, 29387, 29399, 30137, 30851, 31181, 31247, 31391, 31511, 31721, 31727, 31769, 31847, 32027, 32057, 32117, 32141, 32321, 32369, 32531, 32561, 32717, 32801, 32831, 32909, 32939, 33071, 33179, 33287, 33587, 33749, 34031, 34033, 34211, 34259, 34367, 34369, 34511, 34757, 34847, 35051, 35081, 35447, 35507, 35591, 35837, 35897, 36467, 36527, 36791, 36899, 36929, 36931, 37019, 37021, 37199, 37571, 37589, 37781, 38567, 38669, 39041, 39341, 39371, 40037, 40637, 40697, 40849, 41141, 41201, 41231, 42407, 42641, 44531, 45137, 45341, 46181, 47351, 47387, 47657, 47699, 47807, 48407, 48539, 48779, 48989, 49667, 49991, 50591, 51059, 51421, 51437, 51479, 51767, 53147, 54917, 55337, 55619, 55931, 56477, 56921, 58109, 58787, 59021, 59051, 59207, 59219, 59627, 60257, 60647, 60659, 60887, 60917, 62141, 62927, 63389, 63587, 63647, 64577, 64781, 64877, 65027, 65099, 65171, 65447, 65537, 65699, 65717, 65837, 65981, 67217, 67577, 67757, 68207, 69257, 69491, 69497, 69737, 69761, 69827, 69857, 69929, 70121, 70181, 70199, 70379, 70877, 71807, 72167, 72221, 72647, 73037, 73061, 74201, 75209, 75989, 76001, 76259, 77237, 78137, 78437, 80627, 80681, 81017, 81281, 82037.

Some larger examples :