## Everything Linguists Ever Wanted To Know About Prime Numbers*

#### *but really shouldn’t have asked

### Adapted by A. Nonymous, Linguist

from various primary sources

How do various types of linguists go about analyzing, for themselves and their conspecifics, the primality of odd numbers greater than one? The methods vary by discipline, but the results are all equally valid.

**The Autosegmental Phonologist**
- Like the other odd numbers, 9 is underlyingly specified for the feature [prime], but 9 surfaces as composite because of an [even] feature spread from 8.

**The Corpus Linguist**
- 3 is prime, 5 is prime, 7 is prime, 9 is not prime, 11 is prime, and 13 is prime. Thus, in our corpus, odd numbers are prime at a probability of 0.833.

**The Formal Semanticist**
- Let the universe of discourse be the natural numbers less than 8...

**The Functionalist Syntactician**
- How can you say that all odd numbers are prime when we have a clear counterexample in the case of 6?

**The Historical Linguist**
- It is clear that the whole paradigm of odd numbers was originally prime (see, for example, 3, 5, 7, 11, and 13). However, certain composite numbers, including 9, have been introduced into the paradigm, probably through borrowing.

**The Jaded Syntactician**
- 3 is prime, 5 is prime, 7 is prime. 9, 9, hmm, 9, hmmmm... Yeah, I guess I can get 9 as prime.

**The Lab Phonetician**
- 3 is prime, 5 is prime, 7 is prime. 9 is not prime, most likely due to an aberration that will disappear after we test more subjects. 11 is prime, 13 is prime...

**The Linguistic Logician**
- Hypothesis: All odd numbers are prime.

Proof:

1. If a proof exists, then the hypothesis must be true.

2. The proof exists; you’re reading it now.

From 1 and 2 follows that all odd numbers are prime.

**The Minimalist Syntactician**
- 3 is prime, therefore, by induction, all odd numbers are prime.

**The MIT Linguist**
- The assertion that 9 is not prime is not explanatory. It is, at best, descriptive.

**The Phonologist**
- 3 is prime, 5 is prime, and 7 is prime. While 9 does not appear to be prime, if we said it is not prime, we would be missing an important underlying generalization. Therefore, 9 is prime at a more abstract level.

**The Structuralist**
- While 3 is prime, 5 is prime, and 7 is prime, 9 is not prime; therefore odd and prime are in contrastive distribution and can be used to distinguish morphemes.