Malema's matric and Home Affairs

The matric (school-leaving exam in SA) results of Mr Julius Malema, leader of the ANC Youth League, have been circulating in the country over the past week or so. This gentelman, who is famously prepared to "kill" to support "the revolution" managed to get 4% (an H symbol) in the exam in Standard Grade Mathematics. He did manage 57% in History (also on Standard Grade) which is, presumably, more important for a politician. Now, I do not doubt that there were not many opportunities for academic advancement where Mr Malema grew up and although he should perhaps have tried better nevertheless, I am most surprised that no-one has commented about the spelling of "mother tongue" with a Q on the, apparently, official print-out.

Lest anyone believe that the spelling mistake or typo indicates the Malema document not to be genuine, I present the image on the left from an official receipt from the Department of Home Affairs (for a passport application), dated earlier this month. Somehow they got the Afrikaans for "affairs" as "sakke" (meaning "bags") instead of "sake". I have to wonder whether this is the case at every office of Home Affairs or whether it is only at this office and - in that case - whether all the offices set up their cash registers or printers manually.


Also see

1. "Malema’s (lacklustre) matric results", The Sowetan, 2008-10-24, http://www.sowetan.co.za/News/Article.aspx?id=870114

Prime number formulae

Last week, I was interviewed on ClassicFM in the show The Internet Economy about GIMPS - the Great Internet Mersenne Prime Search. During the interview, I said that there was no formula for generating prime numbers, by which I meant - of course - that there is no easy formula. As Eric Weisstein writes in the authoritative MathWorld,

"all such formulas require either extremely accurate knowledge of some unknown constant, or effectively require knowledge of the primes ahead of time in order to use the formula."

He is writing about formulae that are known to produce the n-th prime p(n) on input n. There are other kinds of prime-generating formulae. Consider, for example, the formula described by Eric Rowland in a recent issue of the Journal of Integer Sequences. Rowland's sequence is defined by

a(n) = a(n-1) + gcd(n, a(n-1))

and a(1) = 7. He shows that the values taken on by a(n)-a(n-1) are always either one or prime. However, it is not known whether all primes are produced by this sequence, and I expect it not to be the case! Another approach is to consider the values taken on by a polynomial with integer coefficients and in several unknowns. There exist polynomials for which all the positive values are all prime and in fact there exist such polynomials for which all prime numbers are found among the positive values. These prime-generating polynomials (about which more in the MathWorld article cited below) are, however, not a particularly efficient way of generating prime numbers.


Sources

1. Podcast of the 3 October 2008 edition of The Internet Economy on ClassicFM http://tinyurl.com/3m2gug
   


2. Weisstein, Eric W. "Prime Formulas." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PrimeFormulas.html
   


3. Rowland, Eric S. "A Natural Prime-Generating Recurrence." Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8 http://www.cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21.html
   


4. Weisstein, Eric W. "Prime-Generating Polynomial." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html