Sorry, an error occurred while loading the content.

## RE: [PrimeNumbers] RE Love prime numbers; have a question

Expand Messages
• ... A witness for n is a witness to its compositeness (there must be a better word than this for non-primality!) so the RH-related statement above doesn t
Message 1 of 5 , Nov 19, 2005
>From: Jose Ram�n Brox <ambroxius@...>
>To: "Prime Numbers" <primenumbers@yahoogroups.com>
>Subject: [PrimeNumbers] RE Love prime numbers; have a question
>Date: Sat, 19 Nov 2005 14:54:44 +0100
>
>----- Original Message -----
>From: "Jose Ram�n Brox" <ambroxius@...>
>
>Indeed, Carmichael fails Fermat test and therefore qualify as a-PRP, but
>not all
>Carmichaels are a-SPRPs. I also think the infinitude of SPRs is still
>undecided.
>
>---------------------------------------------------
>
>Following Mathworld, if the RH is true, any composite n would have a
>witness (an x so that
>n is x-SPRP) less than 70�(log n)^2. That would imply the infinitude of
>SPRPs since every
>composite would be a SPRP for some base a, though It would leave open the
>question "Is
>there a infinity of a-SPRPs for every base a?"

A "witness" for n is a "witness to its compositeness" (there must be a
better word than this for non-primality!) so the RH-related statement above
doesn't actually say anything about whether a composite n must be SPRP to
any base a, merely that it will fail to be SPRP to a base a less than
70(logn)^2. (Hasn't this bound been improved? I'm sure I saw a better result
somewhere...)

Richard
Your message has been successfully submitted and would be delivered to recipients shortly.