Is there no test for a number that is Prime?

This is just scratch work. It is not in working form. However it is my attempt to write a trap door function. The problem is the enciphering of the message that needs encrypted. Also I do not know if the one way function can be mathematically difficult.

The encryption part is not the numbers of the odometer itself. Instead I am trying to use the numbers between the odometer reading. For example how many digits change between 2 readings.

My approach here is linear, but there is no reason the odometer readings could not be set to some sort of pattern maybe even out of order.

This was confusing to create. It could be wrong. And it may have flaws easy to defeat, but hard to design. So bare with me if it is nonsense. I am completely serious. I just wanted to get feedback, because writing it it makes sense, but the question I need to know is if it is mathematically possible.

Now that I have written this idea out. And that is all it is, an idea, I need to research trap door functions. This is how I envision the Enigma Machine or M205 working. However they were not public key. So if you care to comment or list other trap door functions, reply.

Take the odometer problem where at least 2 digits repeat and you may be able to create a trap door function.

The public key would be the number of digits of the length of the odometer numbers. If you add this key to the message then this new odometer reading is the encrypted message.

The private key is a lower number on the odometer. This number is subtracted from the public key and subtracted from the larger encrypted odometer. This gives the unencrypted message.

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Second Method:

Public key is a random odometer reading.

The message is encoded using this random odometer reading.

The private key is a random odometer reading, which the distance between the public key random odometer reading is known.

The private odometer knows the distance between the private and public key. The difference minus the public key reveals the public key.