Each of A, B, C, A+B*C, B+C*A and C+A*B is a prime number.

Find the possible remainders when A+B+C is divided by 6.

(In reply to

sum not product by xdog)

Apparently I've solved a wrong QUESTION and even there missed the case of 2,3,C , C being an odd number bigger than 3.

So the answer is (A,B,C)=(2,odd1,odd2) with the possibility of one of the odds being 3 and ignoring the symmetrical solutions.

THEN:

SUM (A+B+C) can be any of 0,2,4

PRODUCT (A*B*C) - 2,3, or 4