# Listen With Others

## Listener No 4660: Prime Cuts by Zag

Posted by Dave Hennings on 11 Jun 2021

The last Zag Listener was that (thankfully) rare instance of a mathematical Playfair puzzle. This week, we had to deal with numbers from which 2-digit primes needed to be removed before entry in the grid.

The starting point was 15ac where the 5-digit answer was the cube of prime D with prime L being removed to give the square of prime S. A quick examination of D from 23 (lowest 5-digit cube of a prime) to 43 (highest 5-digit cube of a prime) revealed that only D = 23 or 29 worked, with 121(67) and 2(43)89 giving S = 11 or 17. 10dn with ascending digits precluded 121(67) since it could not end in 2.

As usual, I will leave a detailed analysis of this Listener mathematical to my co-bloggers and listenercrossword.com.

The enjoyable feature of this puzzle was that, using Adrian Jenkins’s The Number File, simple scanning of the entries under “Squares of integers to 100”, “The first 200 triangle numbers” and the two pages of primes, together with limited calculator checking was all that was needed. Obviously, those of you anticipating a more taxing mathematical would have been disappointed, but no doubt the next one will appease them!

Mind you, it wasn’t a particularly quick solve and my notes ran to six pages.

Thanks for a gentle quarter, Zag.