Prosperity was chartered in 1851 under the name Frog Level. The name was changed to Prosperity by popular demand in 1873.
There were 415 households out of which 33.5% had children under the age of 18 living with them, 46.0% were married couples living together, 19.5% had a female householder with no husband present, and 29.2% were non-families. 26.3% of all households were made up of individuals and 13.3% had someone living alone who was 65 years of age or older. The average household size was 2.51 and the average family size was 3.01.
In the town the population was spread out with 27.8% under the age of 18, 7.1% from 18 to 24, 29.1% from 25 to 44, 22.0% from 45 to 64, and 14.0% who were 65 years of age or older. The median age was 35 years. For every 100 females there were 78.4 males. For every 100 females age 18 and over, there were 77.5 males.
The median income for a household in the town was $30,875, and the median income for a family was $39,261. Males had a median income of $31,406 versus $19,226 for females. The per capita income for the town was $15,323. About 14.6% of families and 16.9% of the population were below the poverty line, including 22.5% of those under age 18 and 14.9% of those age 65 or over.