Karim BELABAS on Tue, 17 Sep 2002 19:25:07 +0200 (MEST)

 Re: nextprime/precprime

```On Tue, 17 Sep 2002, Jon Perry wrote:
> Why does Pari give:
>
> ? nextprime(7)
> %1 = 7
> ? precprime(7)
> %2 = 7
>
> This behaviour is stated in the user guide, but no justification is given.

The user's guide defines

nextprime(x) = min { p >= x, p prime },

as opposed to the perhaps more natural

nextprime2(x) = min { p > x, p prime }.

[ likewise precprime ].

I have no real idea why this was originally done that way. Probably because,
in the french language, when you say p is greater than x, you usually mean
"larger or equal" (likewise the french word for "positive" means ">= 0").

It's probably unfortunate (all major systems I know of have a nextprime2():
maple, Mathematica, magma, etc.), but it can hardly be changed now.

Karim.
--
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
Dép. de Mathematiques, Bat. 425  Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
--