(a) 23 = 1 × 23,
23 has only two factors 1 and 23, Therfore, it is a prime number.
(b) 51 = 1 × 3 × 17,
51 has three factors 1, 3 and 17, Therfore, it is a composite number.
(c) 38 = 1 × 2 × 19,
38 has three factors 1, 2 and 19, Therfore, it is a composite number.
(d) 26 = 1 × 2 × 13,
26 has three factors 1, 2 and 13, Therfore, it is a composite number.
Hence, the correct answer is option (a).