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Technically that depends on how "prime" is defined. The proper definition (roughly "has a prime factorization of cardinality exactly one") doesn't include one (
by a1369209993 3y ago
Technically that depends on how "prime" is defined. The proper definition (roughly "has a prime factorization of cardinality exactly one") doesn't include one (and for good reason), but the version typically(?) taught in school ("has no factors other than one and itself") obviously does. A LLM could legitimately assume you mean "prime"-as-defined-by-mathematically-illiterate-math-teachers, rather than actually prime, and it would be in good company, since many bright school children have assumed the same.
- contravariant 3y agoOf course it depends on the definition but none of the ones still in use consider it a prime. It's kind of hard to nail down precisely why, the best I've been able to come up with is that Z/(p) is an integral domain for all primes p (and this is roughly equivalent to the definition of a prime) but not for p=1. Furthermore if you then plough on and redefine the Z/(1) i.e. zero ring to be an integral domain it becomes a pain to construct its field of fractions. Arguably 0 is a better prime, as it is a prime element.
- a1369209993 3y ago> none of the ones still in use consider it a prime. "has no factors other than one and itself", AFAIK, is still used by school teachers (and others) introducing the concept of prime numbers. I agree that that definition is wrong, but that wasn't the point I was making.