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Finally completed. I was extremely close much earlier in my attempt, but I foolishly gave up on trying to jiggle the last few digits to make the totals come out right.

Please could somebody give me the sum of the digits for 10a?

bananabean ..... 37 is your total

How many primes in each row?
I think I know Rows 1, 5, 6 and 7
How many partitioned primes in rows 2, 3 and 4?

Row 2: 4
Row 3: 3
Row 4: 4

Well that was fun. After three days I’ve finally given up.
This puzzle should have been called “Eric Morecambe”, because I, like a few others presumably, have “the right numbers - but not, necessarily, in the right order”. At least my effort satisfies 18a.
Congratulations to all who finished this.

If anyone is still looking at this thread I wonder if there is a chance that they could offer any advice.I haven’t been able to successfully complete this crossword, but for a clue such as 1d with a multitude of possibilities is Excel able to select possible answers of which you know the final two digits. My attempt to solve this crossword has extended to the task of trying to learn how to use Excel effectively.

Hi Casanova. Excel can certainly help to narrow down the search for the bigger numbers... I’d go as far as saying it’s crucial. My excel skills are limited so I enlisted him indoors for this element and he took on the task with gusto. How many of the clues do you have left to solve? I found that, once we were getting close to the finish, and with three of the 25 different primes we’d got being 3 digits, some analysis of the the sum of primes between 1 & 100 helped. I identified which of the 1 to 100 primes needed to be excluded to make the sum work, found what I’d got left and then did some blue peter cutting out and jigsaw trial and error until it all fell in to place. Good luck with getting it finished. I’ll keep checking back in case you post for further help.

Hello Merenz. Thank you for the feedback. I have a number of clues to solve still, and I am not sure of the logical necessity of those I have solved. I have tentatively that 1d ends with the digits1 and 1 and commences with a 5. That means that the prime must end with 1 or 9. There are, therefore, 10 possibilities for the prime. So there are a multitude of possibilities for 1d. I think you must be talking about the final partitioning into primes when you refer to analysis of addition of primes between 2 and 100. I haven’t reached that stage of the solution as of yet.

Hello Merenz. Thank you for the feedback. I have a number of clues to solve still, and I am not sure of the logical necessity of those I have solved. I have tentatively that 1d ends with the digits1 and 1 and commences with a 5. That means that the prime must end with 1 or 9. There are, therefore, 10 possibilities for the prime. So there are a multitude of possibilities for 1d. I think you must be talking about the final partitioning into primes when you refer to analysis of addition of primes between 2 and 100. I haven’t reached that stage of the solution as of yet.