# Listen With Others

## Primordial by Viking, Enjoyable numbers!

Posted by shirleycurran on 17 September 2010

Anticipating this one ruined my week. (Yes, I can hear you, “Get a life!”) It is frightening how addictive this Listener habit has become, though I am capable of kicking the habit with the three-monthly numericals.

Surprisingly, Viking’s ‘Primordial’ looked relatively approachable. We didn’t even need the Internet to identify all the ‘distinct prime numbers with all their digits odd’. The university Handbook of Mathematical Tables and Formulas (Burlington) came out and we soon had our list.

From that point on, there was work to be done identifying the two and three-digit twin primes, the palindromic triples, the  two and three-digit mirror-image pairs and the double-digit primes (and, of course, very tellingly, the numbers that figured in none of those lists).

We attempted our grid fill and found ourselves going round in circles. There had to be a unique solution that would give us our starting point, but we seemed to come up against ever-increasing possibilities or dead ends. After several false starts, Mr Grumpy went to bed with “Tomorrow will be soon enough!”

We had recognised two useful pieces of information. Only ten two-digit answers were clued but there were twelve spaces and two primes, 59 and 53, that were not in our list and had to go into the unclued lights at 32ac and 20dn. The primes 191 and 313 also fixed themselves in either 8dn or 24ac, since they were the only two that occurred in lists of both ‘three-digit twin primes and three-digit palindromic primes’. ” That gives four different possible combinations”, announced Mr Math before retiring.

I must have attempted the other three before suddenly hitting lucky. Opting for 59 in 32ac and working from there, via the three-digit mirror image pairs, (rather a trial and error system – there must have been an easier way!) I suddenly hit on a fit up at 6ac and 6dn, where the mirror images went and managed to move across to 8dn where we had a putative 191 – that was confirmed!

From this point on, it was magic – just like the massive jigsaw puzzle that sits on the table at Christmas with the picture becoming clearer as the pieces slotted in. I believe those pairs (71/73 at 15ac 41dn, for example) confirm some sort of Heisenberg certainty principle, where you slot one in and the other miraculously wings its way to the other side of the puzzle. They were certainly very welcome confirmation that I was on the right track.

The mathematical half of the team (happily dreaming by this time) had said, “It is important to keep track of what you are doing”. The highlighted list was invaluable at this point, as, when all the clued answers had gone in, there were little gaps and several primes that were in no clue at all. This was where my admiration for Viking developed. Of course, the extra numbers filled the remaining lights. How did he work out that it was possible to fit ALL the odd digit primes into one 9 X 9 symmetrical grid?

I can imagine that the Magpie E solvers are harumphing and muttering ‘Too easy’ but the verdict of a number numpty is that this was tremendous fun and a superb way to convince those of us who go into hibernation once every three months, that the numericals are possible.

1. ### erwinchsaid

Well, I am glad that you liked Primordial Shirley but as one who looks forward to the numericals it came as a big disappointment. I couldn’t find enough to say to warrant a separate blog so am limiting myself to this comment.

Your description of it as a jigsaw is apt but it is a description that can be applied to most of the numerical puzzles although the range of the ‘pieces’ is rarely this small (11 to 999, odd numbers only).

I had thought it pleasing that all primes that fitted the clues were used. For a while I had sorted out eight rather than seven double-digit primes (xyy) but then found that I had included the rogue 811! What I had not realised until reading your blog was that all eligible primes in range appear in the completed grid – that is truly a feat of construction.

After the initial sort, the first grid entries came quickly by finding the values that appeared in two clues, 15a, 41d, 43a and 22d. For a numerical puzzle, an unusual feature was the appearance of several unclued entries and three of them were my final entries – 20a, 20d and 21d.

So, a difficult job for Viking but a rather too straightforward job for this solver. Still it is all to the good if it attracts new people to the wonderful Listener.

2. ### erwinchsaid

The range of pieces should of course read 11 to 997, odd digits only.

3. ### Jakesaid

A great puzzle.
Took a few moments, first looking in the wrong direction. Then the PDM came Ahh! prime numbers. My book of curious numbers has a chart at the back which pretty much solved the puzzle for me. A few wrong turns here and there, but all came to light in the end.

Shirley, where did you get, or, what book did the logarithms of primes come from?

4. ### Shirley Curransaid

An antedeluvian university text book of useful numbers, Jake but any modern book of mathematical tables would suffice. I’ll send you the ISBN of that one (if it didn’t predate ISBN numbers)

Jake (and others),

You may be interested in the following page from the Listener site which includes a Table of Primes less than 10000: http://www.listenercrossword.com/HTML/Reference05.html

Dave.

6. ### Jakesaid

Listenwithothers/Dave.

Thanks for the link. I’ve looked around that website, and it ceases to amaze me what’s on that site. It really needs to be updated and rearranged so the pages can be found instantly. Instead of lurking several links in…..

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