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inconsummate n.  and  strong prime

First numbers that belong to both sets:

431, 461, 521, 821, 827, 1049, 1481, 1487, 1871, 1931, 2153, 2591, 2609, 3037, 3251, 3257, 3329, 3371, 3581, 3659, 3697, 3719, 3761, 3767, 3793, 3821, 4049, 4091, 4127, 4157, 4241, 4253, 4271, 4283, 4349, 4649, 4871, 4931, 4967, 5147, 5231, 5297, 5477, 5639, 6037, 6113, 6389, 6551, 6637, 6659, 6997, 7331, 7487, 8147, 8231, 8597, 8663, 8819, 8837, 9041, 9221, 9341, 9371, 9419, 9437, 9587, 9851, 10037, 10331, 10357, 10847, 10937, 11057, 11483, 11549, 11777, 12037, 12041, 12107, 13217, 13259, 13709, 13997, 14051, 14321, 14369, 14387, 14591, 14621, 14627, 14699, 14813, 14843, 14867, 14879, 14939, 15053, 15137, 15187, 15227, 15299, 15641, 15737, 15887, 16001, 16217, 16811, 17021, 17027, 17093, 17207, 17387, 17657, 17681, 17707, 17921, 17987, 18077, 18131, 18143, 18251, 18287, 18671, 19181, 19259, 19709, 19793, 19853, 20147, 20357, 20477, 20507, 20627, 20681, 20717, 20807, 20921, 20981, 21017, 21059, 21317, 21467, 21587, 21611, 21701, 21737, 21767, 22037, 22271, 22481, 22709, 22937, 23537, 23627, 23687, 24317, 24611, 24917, 25031, 25307, 25367, 25439, 25577, 25841, 25847, 25931, 26111, 26153, 26309, 26489, 26951, 26981, 27031, 27281, 27611, 28097, 28109, 28181, 28211, 28277, 28307, 28537, 28547, 28661, 28697, 28751, 28859, 29021, 29101, 29147, 29201, 29207, 29243, 29327, 29387, 29399, 29437, 29741, 29753, 29819, 30137, 30307, 30697, 30703, 30851, 30937, 31147, 31181, 31247, 31307, 31387, 31391, 31469, 31511, 31687, 31721, 31727, 31769, 31847, 32027, 32051, 32057, 32117, 32141, 32159, 32321, 32369, 32377, 32467, 32531, 32561, 32687, 32717, 32801, 32831, 32909, 32939, 32957, 33071, 33107, 33179, 33287, 33587, 33637, 33703, 33713, 33749, 33851, 33911, 33937, 33997, 34031, 34211, 34259, 34367, 34403, 34421, 34511, 34537, 34757, 34847, 35051, 35081, 35099, 35107, 35141, 35381, 35437, 35447, 35507, 35591, 35837, 35897, 35951, 35977, 36131, 36187, 36209, 36293, 36467.

Some larger examples :