Find a 7-digit decimal number such that:
It is prime;
Its sod() is 38;
The sod() of the first 3 digits is the reverse of the sod() of the last 3 digits;
When it is converted from decimal to base-N, where N is any integer from 11 to 36, all 10 numeric digits and 23 different letters appear, but there is never a Q, S, or Z in its base-N representation (for those bases).

These constraints determine a unique 7-digit number.
Find it.

Bonus: what is its pop culture significance?

Note: the sod(N) is the sum of digits of N

(In reply to high hopes dashed by xdog)

That is about as far as I got with my attempt at an analytic solution.  Then I saw the bonus question and remembered Jenny's Number.

Posted by Brian Smith on 2023-07-29 11:01:51