/sci/ - Science & Math

[Anonymous No.4173323]

So /sci/, my friend and I were talking the other day, and we were trying to come up with a way to define an operation on the prime numbers such that it's a group.

The best I was able to come up with is this:

Let <span class="math">\left \{p_{0}, p_{1}, p_{-1}, p_{2}, p_{-2},... \right \}[/spoiler] be the set of prime numbers
(Is the statement "such that <span class="math">p_{0}< p_{1}<p_{-1}<p_{2}<p_{-2}<...[/spoiler]" necessary here?)

Then define an operation ⊕ by <span class="math">p_{i} \oplus p_{j} = p_{i+j}[/spoiler]

Clearly this is a group, since it's essentially addition on the integers.

But to me, this feels like cheating. Is there a "better" way to define an operation on the primes?

[please fuck me up the ass No.4173352]

pi @ pj = pk s.t. pk is the greatest prime less than or equal to pi + pj where 1 and the negative numbers count as primes also

[Anonymous No.4173490]

If you want this operation to form a group, you're also going to need the negative primes, and 0. (inverses and identity)