Abraham is supposed to be the son of Jobe and Mary, though no solid evidence can be found for this connection.

Abraham could be the son of one of four relationships in Gloucester

Peter Lurvey and Ruel Haraden

Joseph Lurvey and Abigail Ingersal

Eliezer Lurvey and Sarah Pool

Jobe Lurvey and Mary Cunningham

All four couples were in the active childbirth phase of their marriage during the years 1736-1756, and each has gaps in childbearing that could have been filled with an undocumented birth around 1750-1756. Of the three, the best studied by genealogists is Eliezer Lurvey, one of the founders of the Fifth Parish Church. The documentation of his children is poor, and there was an article in NEHGR commenting on the order of their birth, with no mention of Abraham. The possibility that Joseph Lurvey is Abraham's father is intriguing because of the large gap between two of this documented children between 1743 and 1754.

A case can be made for Abraham as the son of Job and Mary as well, if he followed the accepted normal naming conventions for children of New England, His second son, traditionally named for the grandfather, is named Job, and his third daughter was named Mary, same as the grandmother.

Arthaud and Helliwell make the case that Abraham is probably he son of Jobe and Mary Cunni