04 December 2007


If you live in the U. S. and pay any attention to the news, you know that there's a mess going on in the mortgage markets, as companies which have lent to "subprime" borrowers are having trouble. And because of the way that the markets work, this has had effects spread far and wide.

But doesn't "subprime" sound like it should be a mathematical term? It seems like it would either mean:

  • numbers which are just less than a prime (let's say numbers of the form p-1, where p is a prime)

  • numbers which are "almost prime" (say, products of two primes)

But what would a "superprime" be? In the first case, the analogous definition is clearly numbers of the form p+1; in the second case, the only extension I can think of is numbers which are products of 0 primes, i. e. the number 1.


Brent Yorgey said...

To me it sounds like a notation: there's x, then there's x prime ($x'$), and then there's x subprime. I guess a subprime mark would look like a "prime", except upside-down.

.mau. said...

what if a superprime is a power of a prime? No, maybe it's better to call it a subprime so that a superprime becomes a unity.

John Armstrong said...

See, there you go thinking "prime" is a property of a number. Numbers aren't prime, ideals are prime. So a subprime ideal might be one contained in a prime ideal.

But in many cases every ideal is contained in a prime ideal, so it may be more useful to say an ideal is subprime if it's contained in a unique prime ideal. Then we recover .mau,'s suggestion that prime powers generate subprime ideals.