109 is a prime. I'm pleased to say that it is a happy, polite and amenable number (for definitions see, for example,

www.numbersaplenty.com/109). It is a Chen prime - that is a prime number

*p* such that

*p+2* is either prime or the product of two primes: in this case 111 = 3 times 37. You may remember that from

Carnival 107, since 107 was also a Chen prime.

109 is the 24th term of

the Euclid-Mullin sequence, a curious sequence of which each term is the smallest prime dividing the product of all the previous terms plus 1. It's motivated by Euclid's proof that there are infinitely many prime numbers. It begins 2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, 2801, 11, 17, 5471, ... and only the first 51 terms of the sequence are known, since the 52nd is the smallest prime factor of a 335-digit number of which the divisors haven't yet been found.

If we express 1/109 as a decimal, the last six digits of the recurring sequence are 853211, which gives us the first six Fibonacci numbers in reverse order.

Now to the Carnival.

It's always good to start with humour. In the last few days, xkcd has been in excellent form: here is

one on teachers' statistics. And having spent much of my life writing mathematical modelling software, I particularly enjoyed

PHD Comics on software testing which, as so often, hits the mark.

GCHQ, the British Government Communications Headquarters which employs many mathematicians, has been in the news recently. Tom Leinster wrote an opinion piece for the April Newsletter of the London Mathematical Society entitled "Should Mathematicians Co-operate with GCHQ?", which can also be found (with discussion) at the n-Category Café.

Max Tegmark's recent book

*Our Mathematical Universe*, which argues that our universe

**is** mathematics, has divided readers: some think it fascinating, others say its hypothesis is untestable and therefore scientifically meaningless. For a typically entertaining discussion (which, if I understand correctly, goes along with both these views) see

Scott Aaronson's blog Shtetl-Optimized on the topic.

(Aaronson's post has the the wonderful title "This review of Max Tegmark's book also occurs infinitely often in the decimal expansion of pi". If you have a slow internet connection, feel free to save time by, instead of following all the links in this edition of the Carnival, simply going through the digits of pi till you find the content. You might find some other interesting stuff on the way: if so, submit it to the next Carnival!)

From deep or possibly meaningless ideas about whether the universe

**is** simply mathematics to a simple question about multiplication: what exactly do we mean by "6 x 4"? Here are thoughts from

reflectivemaths and

flyingcolours.