CRC and Cell Numbers

It is just a cry from the soul.

For almost a year now I have been driving a payment system. And occasionally to customers' questions: “Why didn’t the money come to the phone?”, I answer “And all because you made a mistake 3 times in dialing!”. However, 3 wrong figures are not the limit. I understand everything, people are in a hurry, the software is slowing down, and the queue is pulling in from behind. Yes, I myself am mistaken easily in such situevina. Online number verification does not justify itself, because checking on a gprs modem is unforgivably long.

And then I thought ...

But what if only one digit was added to the cell phone number - the checksum of the number . The client does not need to know why this figure is necessary, for him it is part of his number. Correctness would practically follow from the issue itself. There would be the possibility of offline validation dialing. If you develop the idea, you can add the operator ID to the algorithm for calculating the check digit. This whole thing would significantly reduce the problems of misapplication. The check digit calculation algorithm can be any, not the idea in it.

PS The captain advises to remind that this is just a dream and, probably, it will remain.

UPD1
Maybe for now, make a box next to the phone number in which the color is determined by the checksum of the digits of the number. (Like here with password) Without explanation, just in the hope of a subconscious mind?