The first photo looks like a coarse stone, but the lines on the sides makes me think it's a natural. If you would like more information about the stone, we need a lot of photos. I don't think it's a Thuringian in any case. If you need more information about Thuringians, the SRP wiki and many threads about them have a lot of information.
For a start, you can buy a "Celebrated razor hone", 5x1" stones in boxes, they are not very expensive, and you'll know that you have a Thuri.