Semiprime Chains

The number associated with my diurnal age today is 27578 and it is a squarefree semiprime with an interesting property. Let's consider its two factors and subtract the smaller from the larger factor and apply the same rule to the difference. Keep repeating this process until the difference is not a squarefree semiprime. The result is as follows:$$ \begin{align} 27578 &= 2 \times 13789\\ 13789-2 &= 13787 \\13787 &= 17 \times 811\\811-17 &=794 \\794 &= 2 \times 397\\397-2 &= 395 \\ 395 &= 5 \times 79 \\79 -5 &= 74 \\ 74 &= 2 \times 37\\37-2 &= 35\\35 &= 5 \times 7 \end{align}$$Once we reach 35, the chain of semiprimes terminates between the difference between 7 and 5 is 2 and 2 is not a squarefree semiprime. However, the process does generate a chain of semiprimes:$$27578 \rightarrow 13787 \rightarrow 794 \rightarrow 395 \rightarrow 74 \rightarrow 35$$Squarefree semiprimes like 27578 that produce another five squarefree semiprimes by subtraction of their prime factors belong to OEIS A296812:

A296812    Take a squarefree semiprime and take the difference of its prime factors. If it is a squarefree semiprime repeat the process. Sequence lists the squarefree semiprimes that generate other squarefree semiprimes only in the first \(k\) steps of this process. Case \(k \geq 5\).

The initial members of this sequence, up to 40000, are (permalink):

4786, 5991, 6218, 8351, 9995, 13391, 14367, 15434, 16658, 16706, 18663, 19466, 27578, 28738, 33551, 34082, 34187, 37727, 38823

The numbers marked in red correspond to the case where \(k \geq 6\), although these numbers are not listed in the OEIS. Take 33551 as an example:$$ \begin{align} 33551 &= 7 \times 4793\\4793 - 7 &= 4786\\4786 &= 2 \times 2393\\2393-2 &= 2391\\2391 &= 3 \times 797\\797-3 &= 794\\794 &= 2 \times 397\\397-2 &= 395\\ 395 &= 5 \times 79\\ 79 - 5 &=74\\74 &= 2 \times 37\\37-2 &=35\\35 &= 5 \times 7 \end{align}$$The number in blue in the list above (28738) corresponds to the case where \(k\)=7 and the prime factors of this number are 2 x 14369 which leads us to 14367 (one of the red numbers).

A similar process involving addition of the prime factors could be applied this would lead, in the case of \(k \geq 5\), to this sequence of numbers:

1774, 2566, 2913, 4497, 6382, 6769, 8902, 9286, 10334, 15177, 19357, 28177, 34669, 35913, 37857

Take 1774 as an example where we have:$$ \begin{align} 1774 &= 2 \times 887\\ 887+2 &= 889\\889 &= 7 \times 127\\127+7 &=134\\134 &= 2 \times 67\\67+2 &= 69\\ 69 &= 3 \times 23\\23+3 &= 26\\26 &= 2 \times 13\\13+2 &=15\\15 &= 3 \times 5 \end{align} $$I'm sure some of these numbers could be taken further as with the differences but I'll leave it there for now.