Memory-hard hash functions maybe? Like, you must dedicate 4gb of ram to compute the function. Not a problem for a one-off, but is a problem when reading lots of pages at once.

Or… the site will serve a random seed and the device must compute 4gb of pseudo-random data, then supply a value at a random server-demanded offset.

Do you want your phone to allocate 4GB to read a mailing list?