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According to Jewish apocrypha, Ben Sira was the son of Yirmiyahu’s daughter who became pregnant in the bathhouse from her father Yirmiyahu’s seed. As such, Ben Sira is mentioned by Rishonim and Acharonim with regard to halakhic discussion of the possibility of become pregnant without intercourse, the questions of whether the sperm contributor is considered his father and whether the offspring of parents who are forbidden relations to each other but who are conceived without intercourse are mamzerim, and the permissibility of in-vitro fertilization. He is also of interest because he was the grandfather of Shimon ben Yeshua ben Eliezer ben Sira, the author of the Wisdom of Sirach and possibly the Alphabet of Sirach.
Record seekers have written that because he was born from the absorption of semen without intercourse he was called Ben-Zer`a (בן זרע, "Son of Seed"), and when he grew up he was embarrassed by this name and changed it to Ben Sira (בן סירא), which is the gematria equivalent of Yirmiyahu (ירמיהו).
The Legend of His Birth 
The legend is brought in the apocryphal and (semi-)heretical work the Alphabet of Sirach. The Rambam and others have ridiculed such writings as a waste of time, but other Rishonim did mention it, if only skeptically or as a point in argument.
The tale in Alphabet of Sirach is that Yirmiyahu was accosted in a bathhouse by onanists, who forced him to emit seed into the water. His seed remained viable and his daughter later used the same bathhouse and became pregnant from the bath.
Halakhic Status and Ramifications 
The halakhic rulings are as follows:
- Yirmiyahu was considered his father, and ben Sira his son.
- Ben Sira was not a mamzer.