[tzs]

Let b be the number of bytes per block.

1. Test N blocks of the disk, where N is small enough that you can keep a 128-bit hash of each block of random test data in memory for the duration of the test. You can use the hashes to verify that read data is correct.

2. Then test another Nb/8 blocks using the N blocks from #1 to store 128-bit hashes of the Nb/8 test blocks.

3. Then test N(1+b/8)/8 blocks, using the blocks from #1 and #2 to hold the hashes.

4. Then test N(1+b/8 + b/8^2)/8 blocks, using the blocks from #1 and #2 and #3 to hold the hashes.

...

(Maybe replace the 8's in that with 7's, and in each block of hashes include a hash of the 7 hashes, so you can check that hash blocks are reading back fine?)

[jeremysalwen]

So basically you are demonstrating that the method is more complex than OPs, with absolutely no benefit, which I think was the point.