Search a number
balanced n.  and  weak prime

First numbers that belong to both sets:

19, 139, 601, 647, 661, 677, 709, 2221, 2251, 2357, 2393, 2659, 2699, 2713, 2837, 3221, 3347, 6719, 6793, 6883, 6911, 6983, 7001, 7027, 7193, 7247, 7369, 7433, 7607, 7703, 7793, 8069, 8089, 8123, 8297, 8317, 8423, 8431, 8527, 8539, 8543, 8599, 8629, 8647, 8681, 8783, 8807, 8821, 8933, 8971, 9013, 9043, 9049, 9109, 9137, 9161, 9209, 9257, 9293, 9323, 9403, 9421, 9433, 9539, 9551, 9649, 9697, 9743, 9817, 9833, 10009, 10223, 10333, 10343, 10567, 10601, 10613, 10631, 10691, 10711, 10837, 10891, 10979, 11003, 11119, 11131, 11161, 11213, 11243, 11279, 11287, 11321, 11353, 11399, 11527, 11681, 11689, 11783, 11789, 11813, 11833, 11909, 11927, 12049, 12347, 12379, 12457, 12479, 12491, 12503, 12517, 12589, 12619, 12641, 12721, 12799, 12823, 12829, 12853, 12899, 13009, 13063, 13187, 13249, 13339, 13469, 13477, 13537, 13649, 13711, 13723, 13729, 13807, 13831, 13903, 13921, 13967, 14083, 14153, 14159, 14389, 14411, 14423, 14437, 14449, 14489, 14503, 14537, 14629, 14633, 14683, 14723, 14869, 14897, 14929, 15107, 15233, 15361, 15377, 15401, 15413, 15451, 15497, 15569, 15649, 15733, 15809, 15881, 15889, 15937, 16063, 16073, 16103, 16111, 16529, 16553, 16607, 16831, 16903, 17029, 17257, 17599, 17609, 17761, 17839, 17911, 17929, 18013, 18257, 18289, 18313, 18523, 33119, 33211, 33469, 33623, 33629, 33721, 33769, 33967, 34261, 34471, 34613, 34729, 35053, 35059, 35159, 35227, 35257, 35407, 35449, 35509, 35533, 35731, 35809, 35899, 35933, 35983, 36013, 36073, 36457, 36529, 36643, 37223, 37277, 37423, 37463, 37493, 37549, 37579, 37717, 37967, 37997, 38189, 38201, 38321, 38453, 38501, 38569, 38677, 38729, 38737, 38959, 39139, 39251, 39317, 39451, 39841, 39989, 40013, 40099, 40241, 40289, 40609, 40709, 41023, 41143, 41149, 41179, 41203, 41389, 41627, 41651, 41813, 41863, 41897, 42101, 42139, 42197, 42283, 42379, 42409, 42437, 42571, 42643, 42649, 42773, 43067, 43117, 43159.

Some larger examples :