Semiprime Chains

My diurnal age today, 28213, is a member of OEIS A096003:

A096003: \( \textbf{smallest}\) semiprime which is at the \( \textbf{end}\) of an arithmetic progression of \(n\) semiprimes.

The initial terms of the sequence are:

4, 6, 14, 46, 58, 221, 445, 497, 1211, 1561, 4195, 4393, 6347, 10717, 14233, 28213, 31451, 72965

In the case of 28213, the chain is 16 semiprimes long with a common difference of 354 as shown in the table below  (permalink):

Semiprime    | Factors

------------------------------

22903        | 37 * 619

23257        | 13 * 1789

23611        | 7 * 3373

23965        | 5 * 4793

24319        | 83 * 293

24673        | 11 * 2243

25027        | 29 * 863

25381        | 17 * 1493

25735        | 5 * 5147

26089        | 7 * 3727

26443        | 31 * 853

26797        | 127 * 211

27151        | 19 * 1429

27505        | 5 * 5501

27859        | 13 * 2143

28213        | 89 * 317

The terms in comma separated form are:

22903, 23257, 23611, 23965, 24319, 24673, 25027, 25381, 25735, 26089, 26443, 26797, 27151, 27505, 27859, 28213

28213 is also an emirpimes since \(31282 = 2 \times 15641\) and even the factors of 28213 when concatenated from higher to lower form the semiprime \(31789 = 83 \times 383\).

The next term in OEIS A096003 after 29213 is 31451 and it is at the end of a chain of 17 semiprimes with a common difference of 1860 as shown in the table below (permalink)

Semiprime    | Factors

------------------------------

1691          | 19 * 89

3551          | 53 * 67

5411          | 7 * 773

7271          | 11 * 661

9131          | 23 * 397

10991        | 29 * 379

12851        | 71 * 181

14711        | 47 * 313

16571        | 73 * 227

18431        | 7 * 2633

20291        | 103 * 197

22151        | 17 * 1303

24011        | 13 * 1847

25871        | 41 * 631

27731        | 11 * 2521

29591        | 127 * 233

31451        | 7 * 4493

The terms in comma separated form are:

1691, 3551, 5411, 7271, 9131, 10991, 12851, 14711, 16571, 18431, 20291, 22151, 24011, 25871, 27731, 29591, 31451

After 31451 comes 72965 that is at the end of a chain of 18 semiprimes with a common difference of 3942 as shown in the table below (permalink):

Semiprime    | Factors

------------------------------

5951          | 11 * 541

9893          | 13 * 761

13835        | 5 * 2767

17777        | 29 * 613

21719        | 37 * 587

25661        | 67 * 383

29603        | 7 * 4229

33545        | 5 * 6709

37487        | 19 * 1973

41429        | 17 * 2437

45371        | 59 * 769

49313        | 11 * 4483

53255        | 5 * 10651

57197        | 7 * 8171

61139        | 13 * 4703

65081        | 151 * 431

69023        | 23 * 3001

72965        | 5 * 14593

The terms in comma separated form are:

5951, 9893, 13835, 17777, 21719, 25661, 29603, 33545, 37487, 41429, 45371, 49313, 53255, 57197, 61139, 65081, 69023, 72965