Record Prime v. Non-Prime Digit Trajectory Lengths

In a recent post titled Prime and Non-Prime Digit Sequence in November of 2024, I explained that:

Instead of dealing with odd and even digits, trajectories involving prime and non-prime digit sums can be considered. The prime digits are 2, 3, 5 and 7 while the non-prime digits are 0, 1, 4, 6, 7 and 9.

For example, the number associated with my diurnal age today is 27632 and it has the following trajectory of 3 steps under the prime and non-prime algorithm (permalink):

27632 --> 27640 --> 27639 --> 27636 --> 27636

The trajectory terminates when the number has a sum of primes and sum of non-primes that are equal, here 2 + 7 + 3 = 6 + 6. 

🅃🅁🄰🄹🄴🄲🅃🄾🅁🅈 

What I want to look at this post are the trajectory lengths of numbers under this prime and non-prime digit algorithm. Table 1 shows a plot of the results up to 100,000.

Figure 1: permalink

The lines are not vertical of course. It just means that the new records are clumped together. Table 1 shows the clumping as we jump from 8185 to 14067 which is where some brief clumping occurs (14067, 14077 and 14085) before we jump to 19165 which is where the real clumping occurs, up to 19452. After this there is massive jump 49370 where more clumping occurs.

Table 1: permalink

From the perspective of my diurnal age analysis, the last record occurred when I was 19452 days old and here was its trajectory:

19452, 19445, 19432, 19423, 19414, 19395, 19384, 19365, 19357, 19362, 19351, 19348, 19329, 19315, 19312, 19306, 19293, 19279, 19269, 19246, 19228, 19214, 19201, 19192, 19174, 19166, 19143, 19131, 19122, 19115, 19108, 19089, 19062, 19048, 19026, 19012, 19003, 18996, 18963, 18942, 18922, 18908, 18882, 18859, 18838, 18816, 18792, 18783, 18776, 18775, 18785, 18780, 18770, 18775

The number 19452 is captured by the vortex 18775, 18785, 18780, 18770, 18775. So no more records for me as I am not going to live to see a diurnal age of 49370.