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...and hints, large and small.

Great timing for a numerical! My daughter and grandson are visiting.

Indeed great timing. This the first weekend since before Christmas that we are allowed to go to the pub where I live. Of course, I hope that those who tackle the puzzle enjoy it. See you all next week.

Think I have 15a!
Any other easy ways in?

That's my first one too. Have put it down to watch the rugby and I'm not sure I will pick it up again.

Sad face.
Was trying to find some enthusiasm for our lack of crossWORD.

I think that is the best place to start, Lumen. When you combine the relatively few options for 15a with the information that 10d has ascending digits, I think that settles it. (Unless I missed something.)

The intersection of 11a and 11d might be another place to try.

All sorted, thank you Zag

Having completed the grid unambiguously, I have some uncertainty about three of the original answers. In 7ac and 16dn, there are different answers depending on whether the prime that has to be removed comes at the beginning or the end of the original answer. In 12ac, the prime could come in any of four positions, as the digit sum is invariant to how the digits are arranged.

Have I missed something that would resolve the ambiguities? It doesn't matter for the final grid, and perhaps the wording of the preamble "All answers and entries are different" does not rule out the possibility of multiple answers to individual clues.