Search a number
balanced n.  and  twin primes

First numbers that belong to both sets:

11, 19, 41, 139, 149, 197, 569, 601, 617, 659, 661, 809, 2141, 2381, 2659, 2713, 2729, 3461, 6791, 6793, 6947, 6959, 7487, 7559, 7877, 7949, 8087, 8089, 8219, 8429, 8431, 8537, 8539, 8597, 8599, 8627, 8629, 8819, 8821, 8861, 8969, 8971, 8999, 9011, 9013, 9043, 9281, 9419, 9421, 9433, 9767, 9929, 10009, 10271, 10301, 10331, 10333, 10457, 10711, 10891, 11057, 11119, 11161, 11351, 11353, 11489, 11699, 11831, 11833, 11969, 12041, 12071, 12161, 12379, 12823, 13001, 13009, 13217, 13339, 13397, 13711, 13721, 13723, 13831, 13901, 13903, 13997, 14083, 14387, 14389, 14447, 14449, 14561, 14627, 14629, 14867, 14869, 15137, 15359, 15361, 15641, 15649, 15733, 15887, 15889, 16061, 16063, 16139, 16229, 16831, 16903, 17029, 17599, 17839, 17911, 18289, 18311, 18313, 18523, 33149, 33749, 33769, 34127, 34157, 34259, 34261, 34471, 34589, 34649, 34757, 35051, 35053, 35449, 35507, 35509, 35531, 35533, 35731, 35899, 36011, 36013, 36529, 37199, 37337, 37361, 37547, 37549, 37589, 37781, 37991, 38569, 38609, 38669, 39239, 39509, 39841, 40037, 40529, 41143, 41179, 41203, 41387, 41389, 41519, 42071, 42283, 42409, 42571, 42643, 43321, 43399, 43543, 43577, 43609, 43783, 43787, 43789, 44089, 44131, 44201, 45341, 46181, 46349, 47147, 47149, 47657, 47713, 47777, 47809, 48649, 49277, 49367, 49529, 49991, 50021, 50129, 50263, 50459, 50461, 50969, 51343, 51479, 51769, 52363, 53279, 53549, 53593, 53609, 53899, 54419, 54421, 54497, 54539, 54541, 54917, 55049, 55339, 55619, 55621, 55633, 55819, 57529, 57557, 57899, 57901, 58153, 58391, 58439, 58451, 58453, 59011, 59419, 59443, 59669, 60169, 61469, 62981, 63649, 64577, 131711, 131837, 132047, 132527, 132857, 133979, 133981, 134087, 134837, 135017, 135391, 135599, 135911, 136399, 136603, 136651, 136751, 136811, 136813, 136859, 136861, 137339, 137341, 137909, 138179, 138181, 138451, 138571, 138797, 139201, 140729, 140761, 140891, 140893, 141221, 141499, 141677, 141767, 142157, 142607, 142697.

Some larger examples :