Can you create a list of pairs? Not a list of list

Is it possible to get this:{(x1,y1),(x2,y2),(x3,y3)……} -> This is a list of pairs. Not a list of list.

x would be the input into a function, y would be the output.

If not, I will have to create my own Pair function. Pair[Mod[x,6],{x,1,5}]]->

{(1,Mod[1,6]),(2,Mod[2,6])……} -> {(1,1),(2,2),(3,3)…..}