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Hi Wintonian, I have the same ambiguities although I think you mean 12d. Since there is no other help to resolve these, and the grid resolves nicely, I can only assume that this is intentional. At least, I’m not going to scratch my head further by trying to resolve them.

I've followed a thread of logic using the starting digit of 15 down and 4-digit squares containing reversible 2-digit primes. It has led me to the last digit of 11 down being 6 and there is no way I can reconcile that with its grid entry being G+W. Ah well...

Neophyte, keep going. This is a fine crossword and consists of many logical stages. You are correct that the last digit of 11 down is 6. You should be able to find two two digit primes that add to it. My last clue to be solved was 2 across.

Hi, Splinters,

Yes, I did mean 12dn. I originally thought that 12ac, with the four-digit triangular number ending up in the grid as a two-digit triangular number, would be the way in, but it took some time to get a unique entry for 12ac. Like others, I started the grid with 15ac and then the four answers that were originally squares.

The 6 as the last digit of [11dn] wasn't a problem to me as it could result from the sum of two primes ending in 3 or one prime ending in 7 and the other ending in 9.

Thanks. Just seen my obvious error. Will persevere...

Could I check if anyone has recommendations for numerical crosswords from the Listener archive? I started doing the Listener just over a year back and (unlike several posters!) I always look forward to the next numerical. Would be interested in going back and trying some from the past when time allows. Likewise if there are similar puzzles in other publications, please do suggest.

Thanks tatters : )

Zag and Oyler run a splendid magazine called Crossnumbers Quarterly. I thoroughly recommend it. All of the numerical from the Listener archive are worth trying. They are of a consistently high standard.

Hi Splinters - I'm glad you and Wintonian have the same 3 ambiguities as having finished things off I thought I'd check in & see if anyone else was similarly perplexed. I realise you don't need to resolve all the answers (other than to ensure all differ) but it seems a bit slack, especially as for a total maths dunce completing these things is an uphill battle at the best of times. To those still struggling it shows that anyone scoring greater than my pitiful 'U' in O-Level Maths has no excuses! ;¬))

I'd add that going for my 2nd COVID jab this morning was infinitely less painful than solving this puzzle - and a hell of a lot quicker.

Nothing in the preamble implies that there are unique answers for the clues; as long as you get only one valid set of grid entries, that should be satisfactory.

For example, consider clue 12 down. No matter what, if the prime X is ab and the entry is cde, then any of these would be valid values for the answer to 12 down: abcde, cabde, cdabe, cdeab (unless any of them repeat some other answer) since they all have the same digit sum. There are a couple of other clues where there are two valid answers for the prime-entry pair.