Cryptography.
400-bit moduli in 4.2·10⁹ operations and 800-bit moduli in 8.4·10¹⁰ operations. The 800-bit claims would be 36 bits of work. That would be demonstrable on commodity hardware. For comparison, the two most recent factoring records using CADO-NFS are: 795-bit RSA using 900 physical CPU core years set