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i have the larger one at the top

Yes, the third cell of the lower light (20a) cannot contain C as this would lead to a non-prime value for the crossing 4-celled light (16d).

I’m in a muddle here - if you work out what t is from 1st equation, is it still the same value for the 6th equation, likewise m in 2nd and 3rd equation? Some enlightenment would help! Many thanks

Yes diver, the value of each letter in the 6 equations stay unchanged.
I found the 6th equation most useful at first, as it means that one 9er plus a 2er equals the other 9er plus the other 2er, then you can get motoring along nicely after that.

Also, if you rearrange the top two equations, then you will see that all the six 4ers add up to s+m-7+5t+c+n. I promise this will help right at the end of the puzzle.

Yes, but I'd start with equation 6 to establish t, save equation 1 till nearer the end game.

Thanks for your help. I’d established a, b, s and t and where they should go in the grid as there are only two 2ers and two 9ers, but there are several 5ers so I couldn’t work out where to enter my value I got for m. I’m probably being thick but as the grid entries are 28 distinct prime numbers and there are 16 letters each representing a prime number there are more entries than letters and I can’t see how that works!

You are correct - some grid entries are not letters referenced in the equations. In particular the 3s and the 5s. But once you get into it you find that even though they aren't referenced in the equations there is only one possibility that fits for each entry,

Don't forget that as the two Ds and one M appear in three entries then their cells must either be

(a) unches in three separate lights, or

(b) two unches, with the third being in one of the two lights concerned.

Therefore in the case of m with 5 digits we need to identify a light with 5 cells whose first cell is either unchecked or intersects with a light whose first cell is unchecked. Given that the intersection of 7a (9 cells) and 4d (5 cells) cannot contain an L, then there is only one 5-celled light that is available for m.

Regarding entering the unclued primes, there is a nice interplay between two of the 3-letter and two of the 5-letter entries on the right side of the grid which I didn’t spot at first, thereby creating a slight headache when trying to complete the central ‘cross’ of 13a and 5d. The choice of which letter starts the 3-celled 17d is ultimately resolved by the fact that all 28 primes are different.

Crosswhit - isn’t that slightly over complicating it re the positioning of m?

I could only find one position for it just by looking at it like a jigsaw as its first digit couldn’t intersect with a 3 digit entry and 1A, 3D and 4D wouldn’t fit with other entries already in