Crossword Help Forum
Forum Rules

Hi s_pugh. I have fully solved this but have also missed what you are referring to in relation to 16D. Please enlighten.

RobP86 - look at the clue and look at the solution...

... the digits...

... the digits...

Why did it post my reply twice?

Thanks Smartie - Sometimes you can't see the blindingly obvious

The common feature of the solutions implies that they are all of form 4k+1.

This includes them all : http://compoasso.free.fr/primelistweb/page/prime/liste_online_en.php

Can someone more mathematically knowledgeable than I am explain how the endgame is solveable without the internet site that calculates sums of squares for a given number. There are twenty 9-digit numbers in the grid, and many (perhaps most) of them take the form 4k+1 so are possible candidates. How does one test each one in turn without that internet aid? If it's essential I don't regard that as fair.

Alternatively one can take symmetrical pairs of 4- or 5-digit numbers, square and sum them to see if they match any 9-digit numbr in the grid, but there are an awful lot of 4- or 5-digit numbers in the grid. There are 90 5-digit numbers in the rows and columns alone, ignoring diagonals.

My Casio scientific calculator (cost about £9) handles sufficient digits and does prime factorisation so I was able to check the 22 9 digit numbers and identify those that were prime. I assumed (perhaps not totally justifiably) that each of the pairs of positive integers were symmetrically placed, so had to have 5 digits. That allowed me to figure out the maximum value for the bigger of each pair, and given the symmetry find them relatively easily.
So it is perfectly possible without the internet, though you might debate whether you should need a scientific calculator.