io.write("Enter the limit: ")
local n = tonumber(io.read())
local sieve = {}
for i=2,n do sieve[i]=true end

for i=2, math.floor(math.sqrt(n)) do
    if sieve[i] then
        for j=i*i,n,i do
            sieve[j] = false
        end
    end
end

print("Primes up to "..n..":")
for i=2,n do
    if sieve[i] then io.write(i.." ") end
end
print()