There is at least one distributor interested. (“at least” means “a minimum of”)
At least there is one distributor interested. (“at least” means “fortunately, happily”)
Are the explanations correct?
When my teacher taught me about focus adverb, she explained, “The position of the adverbs can change the meaning of the sentence.” And she showed these sentences as the examples. But I could not find the difference between these two sentences.
The prepositional adverbial phrase “at least” has at least two meanings.
at the lowest estimate or figure.
at any rate; in any case: ‘You didn’t get a good grade, but at least you passed the course.‘
Usually it is placed before a number when it means No. 1 and placed at the beginning (or end) of a sentence (sometimes without any number as the above example shows) when it means No. 2.
Your example could be rephrased to:
In any case (if nothing else), there is one distributor interested.