Using each of the nine non-zero digits exactly once, form prime numbers such that the sum of these prime numbers, and separately the sum of the single-digit prime numbers among them, is as small as possible.
a) Considering 1 as a prime number.

The digits 2, 4, 5, 6, and 8 cannot be the last digits of our multi-digit base numbers, but 2 and 5 can appear as single-digit prime numbers, while 4, 6, and 8 must be paired with one of the digits 1, 3, 7, and 9 to form two-digit prime numbers. Since the sum of the single-digit prime numbers must be minimal, 1 is included among the single-digit base numbers, and 43, 67, and 89 are the only possible solutions. $1+2+5+43+67+89=207$. (The sum of the single-digit numbers is 8).

b) If we do not consider 1 as a base number - and this is the more sensible and generally accepted approach - then with similar reasoning, we arrive at the following two solutions:

$2+3+5+41+67+89=207$

and $2+3+5+47+61+89=207$ (in both cases, the sum of the single-digit numbers is 10).