the mining is a problem. It takes a lot of electricity to verify a set of transactions and to thereby earn some additional mined bitcoin. I can’t see how this could ever scale up to where it could handle serious transaction volume. It would seem to be too inefficient.
You are thinking about these “transactions” the wrong way.
Consider the person buying an oil tanker full of oil. They need to pay the person in Saudi Arabia (or wherever). Currently they “wire” money from their bank (and pay a fee) to a third party, who converts dinars to dollars (for a fee) and then wires it to the third party (for a fee.) This process takes, literally, days to complete.
This large transaction takes time and fees. A lot of both.\
In the Crypto world, they agree on the value of the crypto for the amount of oil. They transfer the “coin” to the other person’s address. The “crowd” looks at the public ledger to make sure that the sender has the coins to send, and then deducts them. And then they credit them to the valid account. This is done for a very (relatively) small fee.
This transaction takes minutes—an hour at most—and then the receiver is free to convert it immediately into their local fiat, gold, or just leave it in their account.
When you look at the amount and number of very large transfers the crypto process is more efficient, faster, and cheaper. Plus you do not deal with currency conversions that are expensive.
For the “cup of coffee” transactions, you would still use a debit card tied to an account—whether that is a traditional account or a hybrid crypto account is still to be discovered.
Bitcoin is not for the consumer, or retail level. But for large Wholesale and large contract transactions—it beats the SWIFT network by a lot.
So it’s not just the prime numbers then, or is it?
To verify that a 29 digit odd number not ending in 5 is prime, you would need to divide by every odd number not ending in 5 up to 10^15.
Although, once you’ve done that, you would have a list of primes, so you’d narrow your search for the next one.