if the number is even, at least two people are lying (serra/stranger), so it's odd. Also its digits have to be different, because otherwise 11 divides it and 11 is congruent to 3 mod 4 (so sudo would be lying) and either SC or SK would be lying.
If the first digit is even, then the second digit must be 7 or otherwise sci and SK are lying. 27 implies SC lying, 47 implies serra lying, 67 implies sudo lying, 87 implies SK lying, and all of them imply SK lying, so both digits are odd and different.
If neither digit is 7 (i.e. if sci lied) then it has to be a twin prime based on serra/SC; the only 2-digit twin primes are (copied from wikipedia) (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73). 11's digits are the same, 13 means SK lied, 17 we don't care about, 19 means SK lied, 29 has an even digit, 31 means SK lied, 41/43 have even digits, 59 means sudo lied, 61 has an even digit, 71 we don't care about, 73 we don't care about. So Scigatt told the truth.
If sudo lied then it still has to be a twin prime, and one with 7 in it. only possibilities are 17 and 71, both of which imply that SK lied. So sudo told the truth.
If SK lied it's also a twin prime, and also one with 7 in it, so 17 or 71. 17 would let everyone but SK be telling the truth; one of the digits is 7, it differs from 19 by 2, it's prime and it's 1 + 16. So SK can be lying iff the number is 17 (71 implies sudo lied)
too lazy to check if serra/stranger could be lying but phrasing implies only one can be.