Supercharged Semiprimes

 There is a set of non-square semiprimes defined by two criteria:

• the two prime factors concatenate in either order to form two new semiprimes
• the digits of the two prime factors can each be rearranged to form semiprimes

28291 is an example of such a semiprime. Let's examine its properties where || represents concatenation:$$ \begin{align} 28291 &=19 \times 1489\\ 19 \, || \, 1489 &= 191489 \\ &= 53 \times 3613 \\ 1489 \, || \,19  &=148919 \\ &= 137 \times 1087 \\ 19 &\rightarrow 91 \\&=7 \times 13 \\1489 &\rightarrow 1894 \\ &= 2 \times 947 \end{align}$$Up to 40000, the semiprimes that meet both criteria are (permalink):

779, 817, 1121, 1763, 1957, 2071, 2869, 3173, 3403, 3629, 4579, 4687, 4897, 5149, 5977, 6973, 7009, 7181, 7261, 7367, 7493, 8077, 8341, 8413, 8549, 8851, 8977, 9071, 9937, 10123, 10363, 10393, 10679, 10697, 10951, 11051, 11419, 11647, 12407, 12599, 13207, 14317, 14473, 14719, 14809, 14953, 15007, 15143, 15529, 15637, 15751, 16283, 16297, 16321, 16351, 16789, 16873, 17671, 18391, 18563, 18643, 19177, 19247, 19451, 20081, 20311, 20653, 20729, 20989, 21071, 21223, 21733, 21829, 21887, 21971, 22313, 22361, 22489, 22819, 22837, 22879, 22987, 23083, 23351, 23521, 24257, 24377, 24559, 24751, 24757, 24823, 25061, 25843, 25901, 26179, 26239, 26617, 26671, 26969, 27089, 27161, 27199, 27331, 27383, 27589, 27913, 28177, 28291, 28801, 28907, 28937, 28999, 29149, 29329, 29621, 30301, 30571, 30847, 31111, 31921, 32101, 32239, 32293, 32387, 32651, 32699, 33307, 33907, 33991, 34093, 34571, 34579, 34633, 34873, 34927, 35137, 35209, 35341, 35389, 35587, 35701, 35881, 36031, 36199, 36689, 37069, 37127, 37867, 37901, 38021, 38141, 38173, 38323, 38477, 38497, 38989, 39187, 39433, 39707, 39757