Is Columus, OH the only place in the US where 1/2 the population is within 500 miles? Well, kinda

columb.R

# is Columbus, OH really the only place in the US where you're within
# 500 miles of half of the US population?

# claim: https://448f59f74df57015bbb8-a9447b7dfa4ae38e337b359963d557c4.ssl.cf3.rackcdn.com/9987%20Brewdog%20EFP%20Prospectus%20USA%20A4%20v9.pdf
# "Columbus is within 500 miles of over half of the US population"

# get the US 2010 census data
# http://www2.census.gov/geo/docs/reference/cenpop2010/county/CenPop2010_Mean_CO.txt
cent <- read.csv("CenPop2010_Mean_CO.txt")

# make that data spatial
library(sp)
coords <- cbind(cent$LONGITUDE, cent$LATITUDE)
sp <- SpatialPoints(coords)
spdf <- SpatialPointsDataFrame(sp, cent)
proj4string(spdf) <- CRS("+proj=longlat +datum=WGS84")
# reproject
lcc_proj4 <- CRS("+proj=lcc +lat_1=20 +lat_2=60 +lat_0=40 +lon_0=-96 +x_0=0 +   y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs ")
# project using LCC
projd <- spTransform(spdf, CRSobj=lcc_proj4)

# distances between county centroids
distm <- as.matrix(dist(coordinates(projd), upper=TRUE, diag=TRUE))

# iterate over the counties, finding the populations within 500 miles
winners <- c()
for(i in 1:nrow(distm)){
  ind <- which(distm[i,] < 804672) # 500 miles in meters

  # 2010 US population was 309.3 million, there are no counties
  # with > 150 million within 500 miles, so let's say 148 million
  if(sum(cent$POPULATION[ind]) > 148e6){
    cat("HURRAH:", as.character(cent$COUNAME)[i], as.character(cent$STNAME)[i], "is a winner!\n")
  winners <- c(winners, i)
  }
}

par(mfrow=c(1,2))

# plot where that town is
plot(projd, xlim=c(-2.1e6,2e6), ylim=c(-2e6,1.5e6))
points(coordinates(projd)[winners,,drop=FALSE],pch=19,col="red")


# relax that a bit and look for town with >140 million within 500 miles
winners <- c()
for(i in 1:nrow(distm)){
  ind <- which(distm[i,] < 804672) # 500 miles in meters

  # 2010 US population was 309.3 million, there are no counties
  # with > 150 million within 500 miles, so let's say 148 million
  if(sum(cent$POPULATION[ind]) > 140e6){
    cat("HURRAH:", as.character(cent$COUNAME)[i], as.character(cent$STNAME)[i], "is a winner!\n")
  winners <- c(winners, i)
  }
}

# plot where that town is
plot(projd, xlim=c(-2.1e6,2e6), ylim=c(-2e6,1.5e6))
points(coordinates(projd)[winners,,drop=FALSE],pch=19,col="red")

#> unique(as.character(cent$STNAME)[winners])
#[1] "Kentucky"      "Maryland"      "Ohio"          "Pennsylvania"
#[5] "Virginia"      "West Virginia"

Folks from the (albeit population small) non-continential portion of the U.S. might find problems with your analysis.