I am actually not sure how to check status of a specific exponent, maybe only Louie or one of the other admins can do that.
But I wouldn't me too worried if I was you, even if someone else has submitted a result already you (or the other person doing the test) is just making an early double check which has to be done at some point anyhow, so just continue your crunching of the exponent and let the client submit the result it will be useful for the project no matter what.