The primary settlement in Greenville, where over 50% of the population resides, is defined as a census-designated place (CDP) and is located at the junction of New Hampshire Routes 31, 45, and 123.
As of the census of 2000, there were 2,224 people, 879 households, and 556 families residing in the town. The population density was 323.8 people per square mile (125.0/km²). There were 918 housing units at an average density of 51.6 persons/km² (133.6 persons/sq mi). The racial makeup of the town was 97.84% White, 0.27% African American, 0.18% Native American, 0.36% Asian, 0.04% Pacific Islander, 0.13% from other races, and 1.17% from two or more races. 0.63% of the population were Hispanic or Latino of any race.
There were 879 households out of which 32.9% had children under the age of 18 living with them, 49.1% were married couples living together, 9.6% have a woman whose husband does not live with her, and 36.7% were non-families. 29.4% of all households were made up of individuals and 10.7% had someone living alone who was 65 years of age or older. The average household size was 2.53 and the average family size was 3.16.
In the town the population was spread out with 27.4% under the age of 18, 6.7% from 18 to 24, 32.1% from 25 to 44, 22.8% from 45 to 64, and 11.1% who were 65 years of age or older. The median age was 36 years. For every 100 females there were 102.0 males. For every 100 females age 18 and over, there were 104.6 males.
The median income for a household in the town was $39,545, and the median income for a family was $48,750. Males had a median income of $34,792 versus $26,295 for females. The per capita income for the town was $17,901. 7.4% of the population and 2.9% of families were below the poverty line. Out of the total people living in poverty, 5.7% are under the age of 18 and 18.5% are 65 or older.
As of the census of 2000, there were 1,131 people, 465 households, and 279 families residing in the central settlement (CDP). The population density was 333.7 people per square mile (128.8/km²). There were 487 housing units at an average density of 55.5 persons/km² (143.7 persons/sq mi). The racial makeup of the town was 98.14% White, 0.27% African American, 0.27% Native American, 0.35% Asian, 0.09% Pacific Islander, 0.09% from other races, and 0.80% from two or more races. 0.35% of the population were Hispanic or Latino of any race.
There were 465 households out of which 31.6% had children under the age of 18 living with them, 47.3% were married couples living together, 8.8% have a woman whose husband does not live with her, and 39.8% were non-families. 34.2% of all households were made up of individuals and 15.9% had someone living alone who was 65 years of age or older. The average household size was 2.43 and the average family size was 3.15.
In the CDP the population was spread out with 26.1% under the age of 18, 7.4% from 18 to 24, 31.2% from 25 to 44, 21.0% from 45 to 64, and 14.2% who were 65 years of age or older. The median age was 37 years. For every 100 females there were 98.1 males. For every 100 females age 18 and over, there were 101.4 males.
The median income for a household is $42,917, and the median income for a family was $48,889. Males had a median income of $38,875 versus $23,472 for females. The per capita income for the town was $17,850. 5.0% of the population and 1.4% of families were below the poverty line. Out of the total people living in poverty, 3.4% are under the age of 18 and 17.7% are 65 or older.