If you have a leak at the threads of the discharge side of a well pump would it cause the pump to run dry intermittently?

Do you have a submersible pump (in the well) or a jet pump (located above ground). Im betting you have a jet pump. If the intake connection were leaking, then yes, it could cause the pump to run dry. However, if the discharge connection is leaking, the pump will not run dry due to this. The "pump running dry" is a very non-descriptive explanation of what your problem is. When I think "pump running dry" it makes me think your well is running dry.

A leak in the discharge side could cause your pump to lose prime. Is that what you are referring to as "run dry"?

Jl, I have to respectively disagree. A leak in the discharge side could in no way cause the pump to loose prime. The discharge is always located at the top side of the pump, and the check valve or foot valve should always be located on the inlet side of the pump, so a leak on the discharge would not allow water to either siphon or spill out of the pump. A leak on the discharge side of the pump simply couldn't drain the pump, correct? Therefore the pump could not loose its prime in this way.

Now, that being said, I have been wrong way to many more times than I will ever admit. So let me know what you're thinking on this. I suspect I may have to be wrong once again.

You are correct. I am assuming that the poster had a system which was losing prime (running dry) which could point to a leaking footvalve "fed" by a leak in the discharge pipe. We all know the sad history of the word "assume".