Visa and Mastercard numbers are 16 digits. The chances of coming up with a random valid number are very small and that is by design. There is also a checksum built into the card number, which is the first test used to determine whether or not it's valid. (Of course anyone who knows how the checksum works can create a number that will pass the checksum test, so it's mostly useful for preventing data entry errors).
SSNs are only 9 digits. The chances of coming up with a valid SSN are much higher..I believe about 1 in 4, assuming 250 million valid SSNs. There is also no checksum.
Thanks for the very good information. I would hope the SSA is aware of this, and take action to upgrade their system accordingly.
The System was designed in 1935 and is antiqued in many ways. Plus all that patchworks of legislations in attempt to "fix" it.