Primeval Numbers

Today I learned what a $\textbf{primeval number}$ is and it's not surprising that I haven't heard of this type of number before. They are after all rather light on the ground. Here's a definition:

Primeval number: a prime which "contains" more primes in it than any preceding number. Here "contains" means may be constructed from a subset of its digits.

Table 1 shows all the primeval numbers less than 100,000.

Table 1

These numbers form OEIS A072857. After 13679 there is huge jump to 100279.

1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679, 100279, 100379, 101237, 102347, 102379, 103679, 123479, 1001237, 1002347, 1002379, 1003679, 1012349, 1012379, 1023457, 1023467, 1023479, 1234579, 1234679, 10012349

It can be noted that all these numbers are plaindromes or numbers whose digits are in increasing order as required by the definition. For example, 31 contains three primes (3, 13 and 31) as does 13 but the former is not listed because 13 is the first prime to contain three primes.

I was made aware of these primeval numbers via a property of the number associated with my diurnal age today, 27724, that earns it admission into OEIS A173052:

A173052  partial sums of A072857 (primeval numbers: numbers that set a record for the number of distinct primes that can be obtained by permuting some subset of their digits).

These partial sums are:

1, 3, 16, 53, 160, 273, 410, 1423, 2460, 3539, 4776, 6143, 7522, 17601, 27724, 37860, 47999, 58236, 68515, 78882, 89261, 101640, 115319, 215598, 315977, 417214, 519561, 621940, 725619, 849098, 1850335, 2852682, 3855061, 4858740, 5871089