But all of the women have been eliminated from the massive inquiry, which means that the search will continue.
Officers used health records to find any woman who gave birth, or was due to give birth, in the Lothians in the four months in the lead up to when the remains were discovered in undergrowth by a dog walker near Seafield Crematorium, Edinburgh, in July.
Officers also located mothers who elected for home births because their babies' names were not registered on hospital lists.
After the baby boy was found swaddled in a particular blanket bought from Primark officers tracked down about 80 people who had bought the same brand of blanket from the store.
Detective Chief Inspector David McLaren, who is leading the hunt, said conventional lines of inquiry had largely been exhausted.
Officers believe the mother of the baby was a visitor to the city or was just passing through when she gave birth.
Mr McLaren said: "There are about 12,000 births in Edinburgh each year, and we had to trace every mother due to give birth in the three to four-month window before the baby was discovered.
"We are pretty confident the boy's mother never engaged with health services throughout her pregnancy."
Despite the setbacks the 12 detectives are continuing to work on the investigation.