CRC and Cell Numbers

This is just a cry from the heart.

For almost a year I have been driving a payment system. And occasionally to the client's questions: “Why didn’t the money come to the phone?”, I reply, “And all because you made a mistake 3 times in dialing the number!”. However, 3 wrong numbers are not the limit. I understand everything, people are in a hurry, the software is slowing down, the queue is behind them. Yes, I myself am mistaken easily in such a situation. Online number check does not justify itself, because the check on the gprs-modem is unforgivably long.

And then I thought ...

And what if only one number were added to the cell phone number - the checksum of the number . The client does not need to know why this figure, for him it is part of his number. Correctness would practically follow from the number itself. There would be the possibility of offline validation of the set. If you develop an idea, then you can add to the algorithm for calculating the check digit, operator ID. The whole thing would greatly reduce the problems of the wrong set. The algorithm for calculating the check digit can be any, not an idea.

PS The captain advises to remind you that this is just a dream and, probably, it will remain.
')
UPD1
Maybe, for the time being, make a box next to the phone number where the color is determined by the checksum of the digits of the number. (Like here with a password) Without explanation, just in hope of a subconscious?