As many will know, at the start of episodes of the Travels in a Mathematical World podcast I give a number fact. My intention at the start was that I would also point out when numbers are prime, buoyed on by enthusiasm for prime numbers.
In episode 9 of the Travels in a Mathematical World podcast, the first of two in which Dr. Adrian Bowyer talks about his fascinating career, I make an extraordinary claim: 9 is prime. There’s a joke along these lines:
How to prove that all odd integers greater than or equal to 3 are prime.
Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction – every odd integer higher than 2 is a prime.
Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime. Just to be sure, try several randomly chosen numbers: 17 is a prime, 23 is a prime…
Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an approximation to a prime, 11 is a prime,…
Statistician: 100% of the sample 5, 13, 37, 41 and 53 is prime, so all odd numbers must be prime.
Programmer: 3 is prime, 5 is prime, 7 is prime, 9 will be fixed in the next release, …
So I need to apologise for and retract my bold claim. As for an explanation, I do not know what happened! There is also an issue that I say “excluding 1, for which the case is trivial, 9 is the smallest number which is equal to the sum of the digits of its square.” Whereas the entry in trusty Number Gossip tells us 9 is “the only number (except one) which is equal to the sum of the digits of its square” (emphasis added). Now, my statement is not wrong, per se, but strange to have added the extra clause (although my weaker claim is easier to prove by exhaustion, I suppose). I struggle to remember where I got the result from – the reference I give in the show notes for episode 9 points to thesaurus.maths.org, where the result is not claimed.
I think we might just have to assume I switched off my mathematical brain for that week. Anyway, I am grateful to an anonymous poster on the show notes for episode 9 of the Travels in a Mathematical World podcast for pointing out my error. I wonder if the first 294 people who downloaded the episode: (a) didn’t notice; (b) noticed but didn’t tell me; or, I suppose, (c) downloaded the episode but didn’t listen to it. Any of these leaves me a little disheartened.
This also led me to look at the other prime episodes and realise my original intention of noting prime number episodes is erratic at best. Quite apart from the erroneous, I state the fact for episodes 2, 3, 7, 13 and 17 but am guilty of omission in episodes 11 and 19. Episode 23 will be the next maths news episode and we will see if I remember to note the fact.