“When Adam had lived 130 years, he became the father of a son in his likeness, according to his image, and named him Seth. The days of Adam after he became the father of Seth were 800 years; and he had other sons and daughters” (Gen 5:3-4).
The genealogical list in Genesis 5:3-32 continues in the same manner as presented above. That is in each successive generation the antediluvian patriarch—Seth, Enosh, Kenan, Mahalalel, etc.—is said to live X amount of years at which point he gives birth to a son, then he lives Y years further and gives birth to other sons and daughters. Moreover, the genealogical list is enumerated from father to son; there is no mention of the female, and each son is depicted as the first son, who then further fathers a son. This continues for ten generations until we hit Noah. In other words, in this author’s genealogy there is no mention of Cain and Abel. Seth, like Enosh, Kenan, Mahalalel, etc., is presented as the first son.
The genealogy of Genesis 5 was written by the Priestly writer and is part of the interpretive framework that the later redactor imposes on the Yahwist material (also #8-9). We should additionally note that this writer’s genealogy makes no mention of Cain and Abel. If the Priestly writer was familiar with the Cain and Abel story, then it would appear that he has consciously suppressed it. Furthermore, the Yahwist source never explicitly mentions Adam by name, but rather by the generic “the man” (ha’adam). “And the man knew his wife Eve, and she conceived and bore Cain” (4:1). It is conceivable, therefore, that J’s Cain and Abel story, and the genealogy of Adam-Seth were originally components of two separate textual traditions that were later brought together. Genesis 4:25—”And Adam knew his wife again, and she bore a son and named him Seth”—is thought to be a later editorial insertion which attempts to smooth out the tension resulting from the combination of J (4:1) and P (5:3). Needless to say, Genesis 4:25 is at tension with 5:3-4 which clearly implies that Seth was the first born, and if a unified rationale be sought between J and P, then Cain and Abel would have to be born after Seth, at least according to P: “The days of Adam after he became the father of Seth were 800 years, and he had other sons and daughters” (5:4).
There is additionally the same formulaic and thematic interest in Genesis 5:1-32 as was seen in Genesis 1:1-2:4, and expressed in similar terms: creation in image and likeness. These stylistic and thematic similarities fortify the claim that both Genesis 1:1-2:4a and 5:1-23 were penned by the same writer, namely the Priestly writer. Moreover, if P is a later attempt to “rewrite” J, then his lack of acknowledgment of the Cain and Abel story is more an attempt to subvert it, as well as to subvert the history of increasing violence inherent in the Yahwist’s narrative. Rather, the Priestly writer moves us from a good and blessed creation to the flood narrative via a series of genealogies (5:3-23) which in fact merely duplicate the original blessed creation by presenting the generations of mankind from Adam to Noah as a continuation of the creation of mankind in the likeness and image of its creator. There is nothing ominous or corrupt in P’s portrait of mankind, which is radically different from J’s story of fraternal murder and his genealogy of a human race prone to increasing levels of violence and sin.
For more on how and why P imposed a new interpretive framework on J read The Priestly Writer’s Reworking of the Yahwist Material of Genesis 1-11.