Here we will split up any strictly pandigital number (abcdefghij)
and form the general format ab^cdef+/ghij into three parts [ 2  4  4 ]
and test the candidates for probable primeness. Of course
other partitionings/operations are allowed as well like
abc^def+/ghij, ab!+cdefghij, etc.
First case takes place around the keynumber 10.
A pandigital is a 10digit number where all the
digits from 0 to 9 appear once and only once.
The list I compiled is about the (probable)
primes around powers of 10 (complete).
I happened to find exactly 10 solutions (3PRP!).
10^2435 + 9867
10^2569 + 4387
10^5863 + 2497
10^7325 + 6849
10^8459 + 2367
10^2385 – 6749
10^4862 – 9357
10^6354 – 7289
10^6435 – 7289
10^9653 – 8427
Underlined displacements means that the prp's are borderprp's.
The two highlighted prp's show a gem as only the digit 4 is moved.
All 10 exponents and 10 displacements are composite !
[ 2  5  3 ]
Range from 10^23456 –/+ 789 to 10^98765 –/+ 432
Both negative and positive displacements result alas in NO PRP solutions !
[ 2  1  7 ]
The smallest one with a positive 7digit displacement is already prime !
10^2 + 3456789
Starting with base 10 and exponent 2 gives a total of 540 primes.
Quite abundant !
The largest by the way is 10^2 + 9876453.
[ 3  4  1  2 ]
Let me give you another format example of a pandigital PRP
expression. This is the place were you can submit your findings.
(please, avoid the digit 0 as a leading zero)
130 * 2456^7 + 89
[ 2  8 ]
In this section I searched some pandigital expressions
being equal to a palindrome !
10! + 48793625 = 52422425
10! + 49782635 = 53411435
10! + 68593427 = 72222227
10! + 69582437 = 73211237
10!  53628794 = 49999994
10!  73428596 = 69799796
12! + 67938045 = 546939645
12! + 70968345 = 549969945
12! + 87493065 = 566494665
12! + 90847365 = 569848965
12! + 93048675 = 572050275
13!  52793084 = 6174224716
14! + 25639078 = 87203930278
14! + 93526078 = 87271817278
No solutions for 15!, 16! or 17!

[ E  N  D ]