We define non-pandigital expressed
primes so that both the expression and the prime is non-pandigital,
and all digits used in the expression are also used in the prime. We
define the prime as unique if no digit in the expression is
repeated.

Unique non-pandigital prime: A 37
digit prime that excludes the digit 3 and no digit is duplicated in
the expression

6954 x 2^108 - 7 = 2256702022140699458050066967087284217

General non-pandigital prime: An 85
digit prime that excludes the digit 0 with duplication in the
expression (both 6 and 7 are repeated)

27654 x 3^168 - 97 = 3963955326857335459158623686139952966832155324827848754999217785438166562392129386597

We define the quality of the prime as
the ratio of the number of digits of the prime and number of digits
used in the expression.

Thus the Q for above two examples are
37/9=4.11 and 85/11= 7.73 respectively. Solutions using powers of 10
or multiples of 10 are considered trivial

Q. Find other non trivial examples of
higher quality for both types.