[seqfan] Re: -5 is not a prime

[jean-paul allouche]

Dear Neil, dear all

The convention that -1 might be considered as a prime has been used,
e.g., by Conway in his book "The Sensual (Quadratic) Form". On Page 95
for example he writes "Note that we treat -1 as a prime just like the 
others...".
On Page 104, he writes "This includes the case p=-1 if by "prime to -1" we
mean "positive"". This is also used to define Kronecker symbols 
generalizing
Legendre symbols. In other words, it makes several definitions etc. 
"simpler",
but should certainly not be used without caution, as you say about unique
factorizations.

Best wishes
Happy New Year!
jean-paul



Le 03/01/2021 à 18:02, Neil Sloane a écrit :
> Amiram Eldar tells me that Mathematica considers -1 times a prime to be a
> prime.
>
> Select[Range[-10, 10], PrimeQ]
> {-7, -5, -3, -2, 2, 3, 5, 7}
>
> This is wrong, and dangerous (it has led people to make mistakes in
> sequences).
>
> If negative numbers were primes we would lose unique factorization, a
> cornerstone of mathematics.
>
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