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.
3 comments:
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.
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.
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.
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