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I suggest we start a new thread as I am also stuck on 1ac / 7dn.
Can anyone confirm the first two digits of 7dn?

For what it’s worth, I’ve got 13, but I’m not 100% confident.

Yes rad that’s what I have but I’m finding hard to find a suitable 1ac.

I think I have 1ac as 181 squared which seems to work - at the moment!

Yes, 1a is indeed 181 cubed as it's the only one of the few possibilities which ends in 1 and gives 4d as non-prime.

Thanks crosswhit. I am progressing very cautiously and I think I now have 19ac, 18ac and 5dn. Famous last words!

Sounds like you are on the right path Unclued, good luck !

On the basis of what I have so far I don't see how it's possible to partition the grid in a way that is consistent with the preamble. The preamble tells us that the partitioning need not be shown. The implication of that is that it could be shown, and that therefore the existing bars are part of that partitioning. It doesn't say re-partitioned.

However, I have a 5 in the entry for 7d which must be isolated as a solitary prime, and another 5 at the end of 13a. Perhaps that 5 is wrong, but I could find only two squares for 5d that satisfied all the requirements. In one of them the fourth digit was 5, the other 6.

Murky, I may be wrong but your 5 in 7dn is correct. The prime with 5 in at 13ac goes across the bar which is not part of the partitioning. I have 53 for that prime.

Unclued, many thanks for that reassurance. In that case I think the preamble is very misleading It should have used the term, 'repartitioned'.