① There are four possibilities to draw any card from four cards, that is, a number has four digits, namely 1, 2, 3 and 4, of which only 2 and 3 are prime numbers;

(2) Two cards are randomly selected from four cards to form a two-digit number *** 12, but a single number is a two-digit number of 2 and 4, and the sum of these two digits and the digits in the tenth place is a multiple of 3, which is not a prime number; So the prime numbers of two-digit numbers are only 13, 23, 3 1, 4 1, 43;

(3) 2 and 4 are multiples of 2, which does not meet the meaning of the question; Units can only be 1 and 3;

Because 1+2+3=6, 6 is divisible by 3, the three digits obtained by arranging 1, 2, 3 in any order are not prime numbers;

And because 2+3+4=9, 9 can be divisible by 3, so the three digits obtained by arranging 2, 3 and 4 in any order are not prime numbers;

Therefore, the eligible numbers only consist of 1, 2,4: 421; Only one.

(4) Among the 24 four-digit numbers,

Both 2 and 4 are multiples of 2, which does not meet the meaning of the question; Units can only be 1 and 3;

There are: 1423, 1243, 2143,2341,2413,2431,324 1, 330.

* * * Yes: 2+5+ 1+ 12=20 (pieces).