"The U.S. Justice Department wouldn't comment on this specific case, but an agency spokesman pointed CNNMoney to the exact wording of the law, which states that the issue becomes a crime when a person "knowingly possesses, or knowingly accesses with intent to view" child porn. It doesn't appear that an unsuspecting user with these coded links sitting on their hard drive has much to worry about. "
Downloading the blockchain to look at some porn? No? Then no crime.
In theory, "knowingly possesses" means about the same as it does in the drug context: possessing it long enough to know what it is, and yet choosing not to get rid of it. In practice, that kind of case is not prosecuted, or every Usenet provider would have been raided long ago. So in theory, simply having a copy of the blockchain is sufficient, if the blockchain actually contains the illegal content. In practice, I'm not worried about it. I do not believe the blockchain, itself, contains content that it is illegal to possess.