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To be completely clear and spell this out, these fake credit card numbers should not be used to try and purchase stuff.
They merely respect guidelines of a valid credit card number.
I advise you not not to try to use these for any actual transactions, only for testing purposes!
In order to complete a purchase a combination of data must be had, and merely a card number is not enough.
The MOD 10 algorithm is a checksum (detection of errors) formula which is the common name for the Luhn algorithm.For more complete testing data you can make up an expiration dates, a card holder name and possibly an address with a zip code.