What is the smallest number for which it's unknown whether it's prime
or composite?

  Finding this information is surprisingly difficult, even in the modern
era of the internet, which always provides up-to-date information on
everything. If you were to search for the largest known prime, you would
find it in like 2 seconds with google (the vast majority of that time
going into writing the keywords into google). However, I can't find the
answer to my question above.

  (And before anyone starts nitpicking: No, I'm not asking what is the
smallest unknown prime. The difference is subtle, but rather relevant.
You *will* find a few pages which nitpick about this, but they do not
answer the question above.)

-- 
                                                          - Warp

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Warp wrote:
>   Finding this information is surprisingly difficult, even in the modern

Sounds like a good test for Wolfram's Alpha. :-)

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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On Sun, 17 May 2009 10:40:05 -0400, Warp wrote:

>  However, I can't find the
> answer to my question above.

I would guess that that piece of information changes quite frequently.  
Factoring takes time, yes, but there's more than one number being 
factored at any given time...

Jim

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>   What is the smallest number for which it's unknown whether it's prime
> or composite?
> 
>

In my (naive and not very documented) opinion, it should not be so much 
more that the highest prime known (which seems to be 2^(43.112.609) -1, 
if I believe Wolfram) : add 2, or 4, etc. and check if you can obtain 
some trivial factor (like divisibility by 3) - if not then it's probably 
unknown.

At second though, maybe your point is precisely that this smallest 
number with unknown status can be much *smaller* than the highest prime 
known ?

tuabiht

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Jim Henderson <nos### [at] nospamcom> wrote:
> I would guess that that piece of information changes quite frequently.  

  It takes but a few seconds for a website to update for the latest data.
It's not like the internet were a printed encyclopedia.

> Factoring takes time, yes, but there's more than one number being 
> factored at any given time...

  A number begin factored doesn't mean its status is known.

-- 
                                                          - Warp

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Thibaut Jonckheere <tua### [at] mapsonyahoofr> wrote:
> In my (naive and not very documented) opinion, it should not be so much 
> more that the highest prime known (which seems to be 2^(43.112.609) -1, 

  Not all primes between the largest known prime and 2 are known. I'm
interested in what is the smallest number for which it hasn't been verified
if it's a prime or not.

> At second though, maybe your point is precisely that this smallest 
> number with unknown status can be much *smaller* than the highest prime 
> known ?

  A lot smaller.

-- 
                                                          - Warp

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On Sun, 17 May 2009 14:28:56 -0400, Warp wrote:

> Jim Henderson <nos### [at] nospamcom> wrote:
>> I would guess that that piece of information changes quite frequently.
> 
>   It takes but a few seconds for a website to update for the latest
>   data.
> It's not like the internet were a printed encyclopedia.

From which source?  If there are multiple people working on the project, 
some aware of the work others are doing, and some not, you assume that 
everyone working on it keeps everyone updated constantly as to their 
progress.

>> Factoring takes time, yes, but there's more than one number being
>> factored at any given time...
> 
>   A number begin factored doesn't mean its status is known.

Exactly.  See my above comment.

Jim

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Jim Henderson <nos### [at] nospamcom> wrote:
> On Sun, 17 May 2009 14:28:56 -0400, Warp wrote:

> > Jim Henderson <nos### [at] nospamcom> wrote:
> >> I would guess that that piece of information changes quite frequently.
> > 
> >   It takes but a few seconds for a website to update for the latest
> >   data.
> > It's not like the internet were a printed encyclopedia.

> From which source?  If there are multiple people working on the project, 
> some aware of the work others are doing, and some not, you assume that 
> everyone working on it keeps everyone updated constantly as to their 
> progress.

> >> Factoring takes time, yes, but there's more than one number being
> >> factored at any given time...
> > 
> >   A number begin factored doesn't mean its status is known.

> Exactly.  See my above comment.

  Sorry, I didn't understand. "Exactly"? What exactly?

-- 
                                                          - Warp

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On Sun, 17 May 2009 16:47:33 -0400, Warp wrote:

> Jim Henderson <nos### [at] nospamcom> wrote:
>> On Sun, 17 May 2009 14:28:56 -0400, Warp wrote:
> 
>> > Jim Henderson <nos### [at] nospamcom> wrote:
>> >> I would guess that that piece of information changes quite
>> >> frequently.
>> > 
>> >   It takes but a few seconds for a website to update for the latest
>> >   data.
>> > It's not like the internet were a printed encyclopedia.
> 
>> From which source?  If there are multiple people working on the
>> project, some aware of the work others are doing, and some not, you
>> assume that everyone working on it keeps everyone updated constantly as
>> to their progress.
> 
>> >> Factoring takes time, yes, but there's more than one number being
>> >> factored at any given time...
>> > 
>> >   A number begin factored doesn't mean its status is known.
> 
>> Exactly.  See my above comment.
> 
>   Sorry, I didn't understand. "Exactly"? What exactly?

Its status may not be known, but for any individual number that may be 
being worked on, its status may not be known.  It seems there is no 
central place for people to say "I'm working on 
1234567890123435674575623412341413412342323" or "I've just completed 
128347938729759258761923419846957582091841035735235 and it is/is not 
prime".

Jim

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>  What is the smallest number for which it's unknown whether it's prime
> or composite?

1000000000000000000000000000000000

Oh, wait, you just worked out that is composite in your head, so ermm I 
guess it's

1000000000000000000000000000000001

now :-)

BTW, how does everyone else know if such numbers have been tested or not, 
it's not like prime numbers where they are published and announced, people 
probably have done this without publishing the results, so it's just going 
to be some relatively small number that just happens to have never been 
tested by anyone.  Good luck finding out what it is :-)

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