Very Special Five Digit Numbers

Analysing the number associated with my diurnal age means that since I turned 10000 days old, those numbers have always contained five digits and will continue to do so for the remainder of my life. Today I turned 27391 days old and that number has a very special quality.

What's obvious at first glance is that all the digits are distinct but less obvious is the fact the absolute values of the differences between successive pairs of digits, which are digits themselves, are also distinct and are different to the digits of the number. As there are four such differences between the five digits of the number, this means that all the digits from 1 to 9 make an appearance.$$ \underbrace{|2-7|}_{5} \, \underbrace{|7-3|}_{4} \, \underbrace{|3-9|}_{6} \, \underbrace{|9-1|}_{8}$$Numbers of this sort belong to OEIS A365257:

A365257

The five digits of a(\(n\)) and their four successive absolute first differences are all distinct.

The OEIS comments state that:

The digit 0 is never present in a(\(n\)) and never appears as a first difference (as this would duplicate in both cases one of the 8 remaining digits involved).

The sequence ends with a(96) = 98274.

The only prime numbers with this property are 39157, 49681, 51869, 53719, 62983, 68749, 68947, 75193, 78259, 89627 and 95287.

The 96 members of this sequence are:

14928, 15829, 17958, 18259, 18694, 18695, 19372, 19375, 19627, 25917, 27391, 27398, 28149, 28749, 28947, 34928, 35917, 37289, 37916, 38926, 39157, 39578, 43829, 45829, 47289, 47916, 49318, 49681, 49687, 51869, 53719, 57391, 57398, 58926, 59318, 59681, 59687, 61973, 61974, 62983, 62985, 67958, 68149, 68749, 68947, 69157, 69578, 71952, 71953, 72691, 72698, 74619, 74982, 74986, 75193, 75196, 76859, 78259, 78694, 78695, 81394, 81395, 81539, 82941, 82943, 85179, 85629, 85971, 85976, 86749, 87269, 87593, 87596, 89372, 89375, 89627, 91647, 91735, 92658, 92834, 92851, 92854, 93518, 94182, 94186, 94768, 94782, 94786, 95281, 95287, 95867, 96278, 96815, 97158, 98273, 98274

As can be seen, I'm due to experience another such number in a week from today when I reach 27398 days old. My forthcoming 75th birthday, when I am 27394 days old, thus falls between these two special five digit numbers.