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

 8675309 since:

Edited on July 30, 2023, 1:26 am

Posted by K Sengupta on 2023-07-29 02:44:05