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UK National Lottery: now 21% more balls (rounded up)

This week, it was announced that from October the UK’s National Lottery, currently operated by Camelot and already providing a veritable Merlin’s cave of probability lessons for maths teachers, will be changing the rules for its main ‘Lotto’ draw. The main changes are that a new £1m prize will be added to the raffle element you didn’t know already happens, and that matching two balls will win a free ‘lucky dip’ ticket in the subsequent draw. The fixed £25 prize for matching three balls remains on the round table (even though it sometimes causes hilarious number gaffes).

But the Sword of Damocles hanging over Camelot’s changes is that there will be an extra ten balls to choose six from (59 instead of 49), dramatically lengthening the odds of winning all of the pre-existing prizes. This is our round-up of the media’s coverage of this mathematical “news”.

π and the Mysterious Excel Function

Users of Microsoft’s flagship 2D-array-based data-organisation tool Excel will be aware of some if its more recondite functions. From the occasionally useful

RIGHT: returns the substring of a given length from the right-hand end of a cell’s contents

to the wilfully obscure

TBILLPRICE: gives “the price per $100 face value for a Treasury bill” when supplied with its settlement date, maturity date and discount rate

to the downright cryptic

N: obviously, converts its argument to a numeric format if it can

along with approximately 340 others, Excel’s abilities are near limitless.

But one function seems singular in the sheer decadence of its inclusion.

Cédric Villani’s Birth of a Theorem is Radio 4 Book of the Week

Birth of a Theorem, the autobiographical book by French mathematician and (spoiler) Fields Medallist Cédric Villani, is Book of the Week on BBC Radio 4 this week, read by non-French non-mathematician Julian Rhind-Tutt. Villani also appeared on discussion show Start the Week on Monday, talking about ‘the mathematical mind’ along with mathematician Vicky Neale; Morgan Matthews, director of kid-does-maths film X+Y; and novelist Zia Haider Rahman.

New Mersenne primes not discovered

The Great Internet Mersenne Prime Search, the premier distributed-computing prime finding initiative, has reported that $M_{32582657} = 2^{32,582,657}-1$, the 44th Mersenne prime to be discovered, is also the 44th Mersenne Prime in numerical order. It was found by Steven Boone and Curtis Cooper in 2006 (Cooper also discovered the current largest prime as reported here in February), but until now it was not known for certain that other, smaller primes had not been overlooked. GIMPS has now checked all the intervening Mersenne numbers for primality and having found nothing, $M_{32582657}$ is secure in its 44th-ness.

Further information

The Great Internet Mersenne Prime Search (announcement on the front page as of November 10)

Their page for the prime itself

Mersenne Prime at Wolfram Mathworld

via @mathupdate on Twitter

Relatively Prime podcast series 2 Kickstarter

Friend of the Aperiodical Samuel Hansen has launched a Kickstarter to fund a second series of his maths podcast Relatively Prime. The first series was successfully funded in 2011 and consisted of eight hour-long episodes telling “stories from the mathematical domain”, including interviews with Tim Gowers, Matt Parker, David Spiegelhalter and more.

Small gaps between large gaps between primes results

The big news last year was the quest to find a lower bound for the gap between pairs of large primes, started by Yitang Zhang and carried on chiefly by Terry Tao and the fresh-faced James Maynard.

Now that progress on the twin prime conjecture has slowed down, they’ve both turned their attentions toward the opposite question: what’s the biggest gap between subsequent small primes?