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Beulah, the good news is that your digits 1,3 and 4 are correct. So you probably don't need to rework previous answers. (42) is 15659 and (20) is 1786, therefore (21) < 13873.

Digit sums for (21) + (31) = (12) + (40). I make that (21) + 10 = 23 + 9.
So digit sum(21) = 22.

You already have a total of 10 for digits 1,3 and 4, So digits 2 & 5 must total 12. Only one arrangement, that is values 3 and 9 for digits 2 & 5 respectively, satisfies (21) < 13873

Finished! - the clarity of early-morning thought doing the trick, and visiting to see how others are doing. I do agree about how irksome it is to have to re-start numerical puzzles from the blank grid.
It seems many now rely on Internet-borne references but I still use Chambers's (sic) Shorter Six-figure tables, originally bought out of solidarity with my sister-in-law, who had worked for their compiler, L J Comrie, during the war on classified work concerning radar range-finding - a sort of numerical Bletchley Park. Dorothy and my brother were wed in 1947 and the marriage certificate records her occupation as "Computer", to the amusement of the family in later decades.

Thank you so much for your reply. I added (42) and (20) to get the maximum for (21) instead of subtracting! So silly.
Beulah

Thanks to you all for helping me to get as far as i have managed but have come unstuck right at the end. I have three options for 31 (1531,3331 and 4231) which all satisfy 30 and 33. Have I made a mistake somewhere or cannot see the wood for the trees. Wouldn't be the first time ! Would appreciate any hints.

Uncle_W, according to my scribblings, about 7 entries all got resolved when I realised that (26) had to be 813, since the digit sum for (35) had to be less than 15 (value 32n). This then resolved (30) (only 2 options, 354 or 531), which resolved (31), which resolved (13), which resolved (39) and (17)...

Thanks meursault for your reply . I realised that 59 had to be a factor of 30a which meant that only 3331 out of my three options for 31d satisfied the requirement. Thanks again .

Hi oyler. Please would you send me a copy of the original puzzle to franrose23 at gmail dot com.
Thank you so much. I love these types of puzzles.

verlaine, cloverjo. Copy sent.

I have to say I am enjoying this one but glad I have the extra time that sick leave affords! I have made pretty good progress but reached a slight contradiction with 29 and 38. The digit sum for 38 I have as 14 (7+3+4) and I have _16_ for 29. There do not seem to be any primes with that middle that fit the digit sum! I think I must have gone wrong somewhere but can't see where. If someone could please nudge me in the right direction I would be very grateful.

Charlesberg, the six in your 29 is wrong.
Check your possible answers for 37 again.