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swannie - keep in mind that the enumeration after a clue is not the answer length; it's the number of cells and a cell can contain a 2-digit number. So an enumeration of 2 can be as large as a 4-digit number, (3) could theoretically be 6-digits, etc.

What the 2-digit numbers can be is constrained by the fact that every cell gets replaced by a single letter.

thanks, buzzb - got there this afternoon after much sweat. I'd twigged that one of the 2-cell answers had to be a multiple after repeatedly banging my head against what I took to be an impossibility. Then I remembered Holmes's wise remark about unlikely things. A nice final result!

can someone put me out of my misery! finished the logic/prime stuff days ago, but can't do the last bit. checked the maths, increasing order, checked the letters ....am i looking for words? abbreviations? acronyms? are any in the BRB?

Words, but generally not in the dictionary, if you get my drift.

Difficult to say without giving too much away. Not abbreviations or acronyms. Yes in BRB.

As someone said earlier, starting in bottom left and thinking about how things are often hidden in grids did it for me.

You might also note that there's a lot of one particular moderately unusual letter, often found by a second moderately unusual letter and a specific vowel, which might help.

thanks

Late getting to attempt this but I quite liked it. It is actually three almost completely separate challenges. First and most fun was solving the clues and identifying the letter values. Simple logic and no need for electronic aids etc. I ignored 19 and 34 - too hard.
Then populate the grid. Again mainly a logic puzzle but you are left with some ambiguities without 19 and 34.
I put a couple of options into factorisation calculators and decided it was not going to be worth the effort so just did letter substitutions for what I had.
Finally identify the set. The pattern dropped out fairly quickly from the top left and I was able to complete the grid without on line factorisation aids.
Not the usual mathematical Listener but an interesting and clever one.
The set members are hard wired into the brains of people of my age - it may not be quite as easy for younger solvers to spot them.

Well, I finally got there. After a few days of grid-staring, I remembered an inadvertent (?) hint on the other site -regarding the date of publication - which I had forgotten about while doing the solving.

All fun. I guess I’m not of an age where the members are hardwired in my brain.

yes, finally got there, but mostly by a lot of googling, wouldn't have made the connection otherwise. on the positive side, if a future theme is blood groups, dna sequencing or canada i'm prepared.