Try this:
library(geosphere)
cbind(dat, X=rowSums(distm (dat[,3:2],
fun = distHaversine) / 1000 <= 10000)) # number of points within distance 10000 km
id lat long X
[1,] 1 -42.20844 -105.8491530 5
[2,] 2 -23.01770 -116.4395691 5
[3,] 3 13.11361 67.3282248 5
[4,] 4 73.47740 -41.7226614 6
[5,] 5 -53.69725 97.1429112 4
[6,] 6 71.71014 -0.8282728 6
[7,] 7 80.04155 78.3426630 6
[8,] 8 28.94360 177.0861941 5
[9,] 9 23.24053 -43.1873354 6
[10,] 10 -78.87847 99.8802797 4
