Sunday, 13 November 2011

Prime Time

The numbers game
 is too much for Clarke
Fantasy Bob is by no means a mathematician, but from time time he finds himself anorak-garbed and numbers assume great interest.

When Nathan Lyon joined Peter Siddle at Newlands, Cape Town on Thursday, the score board read 21 for 9 (or to their Australian eyes 9 for 21).  This might appear to many a pretty hopeless position but Fantasy Bob notes that they had a chance for glory.  If they added 2 runs and got out with the total on 23, not only would they have scored the lowest total in the history of Test cricket, beating New Zealand's 26 all out at Auckland in 1955, but they would have ensured that the lowest total is a prime number.  This was surely a prize worth clutching.

Instead Lyon and Siddle buckled down and, in the highest partnership of the innings by some way, got the score to 47 before the final wicket fell.  47 is a prime number, so Lyon and Siddle did something right.  But it is not the lowest prime number that has been scored in an innings.  That is 43 which was the total South Africa managed against England in 1889, also at Capetown.  (Capetown is the most regularly occurring ground in the low total tables).

47 is not Australia's lowest total but it is their lowest total that is a prime number.  It is also the lowest prime number total of S Africa, W Indies and New Zealand (all made against England).  England's lowest prime number total is 53 which they scored against Australia at Lords in 1888.  For completeness, readers will wish to know that Pakistan's lowest prime is 59 (v Australia in 2002) and India's 67 (also v Australia in 1948).  By contrast, the highest prime total is W Indies' 751, scored against England in Antigua in 2004.

The S Africa-Australia match abounded in other prime numbers:
  • Michael Clarke scored a superb 151 in the first innings.  151 is a prime number.
  • Graeme Smith scored 101 in the second innings, a prime number.  This is his 23rd Test century.
  • Hashim Amla's 112 in the second innings was not a prime number, but it was his 13th Test century.
  • In their first innings of 96 S Africa scored 89 off the bat and 7 extras - both prime numbers.
  • A number of bowlers, Watson, Harris, Johnson, Lyon, Steyn and Kallis all conceded a prime number of runs from their overs.
As prime numbers go 47 is not a bad one.  Like all prime numbers it has lots of properties.  For example, it is found in a sequence of numbers in which each number is the sum of its predecessors.  The sequence begins 1-3-4-7 and so on.  Both the integers of 47 appear in this sequence.  This makes it a bit more interesting than 43, although 23 is at least as interesting, as well as being the lowest number you cannot get with a single dart.  But less mathematical minds have suggested that 47 is a magic number  - 47 plus 2 equals 49; 47 times 2 equals 94; 49 and 94. That's numbers for you, patterns everywhere you look.  Presumably all these patterns were among the factors that scrambled the brains of the Australian batsmen on Thursday.

Records do not show whether this is the most prime number producing match ever.  FB doubts it, more's the pity.  But the next Test between South Africa and Australia, which begins on 17-11-2011 (3 primes), is Test number 2017.  2017 is a prime number.  2011 and 2017 are sexy primes - ie they are sequential primes which differ by six.  So the stage could be set for some more interesting numbers - and some good cricket.

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