Puzzle 1030. A puzzle cousin of Puzzle 1027

During the week 20-26 February, 2021, contributions to this puzzle came from Oscar Volpatti, Emmanuel Vantieghem and Paul Cleary

I wasn't 100% sure about using digit "0" within a sum, as none of the given example sums involves it.
On the other side, a permitted sum of K=10 integers with no repeated digits is mentioned, but the only such sum is 0+1+2+3+4+5+6+7+8+9.
However, my program could handle different versions of the problem:
digits 0-9 are used at most once (standard?)
digits 1-9 are used at most once, digit 0 is forbidden (harder)
digits 1-9 are used at most once, digit 0 can be repeated (easier)
In each case, I searched up to 10^5, finding both prime and composite numbers with no representations.

Hard version: 16414 composite exceptions, 1741 prime exceptions.

Q1: N = 6088

Q2: P = 10889

Standard version: 756 composite exceptions, 51 prime exceptions (see attached file P1030.txt).

Q1: 6088 = 6087+1, N = 18872
Q2: 10889 = 10857+32, P = 22111

Easy version: 162 composite exceptions, 6 prime exceptions.
Q1: 18872 = 18570+302, N = 22888
Q2: 22111 = 21807+304 P = 78787

As for puzzle 1027, some solutions for numbers before the ones without representations (standard version only)
18868 = 18496+372
18869 = 18596+273
18870 = 18596+274
18871 = 18496+375

22079 = 21695+384
22091 = 21786+305
22093 = 21789+304
22109 = 21769+340