- There is a Law of Small Numbers in statistics,

but you seem to be using the term incorrectly;

just dropping it in where it makes no sense.

Milton L. Brown

miltbrown at earthlink.net

> [Original Message]

wouldn't

> From: D�cio Luiz Gazzoni Filho <decio@...>

> To: <primenumbers@yahoogroups.com>

> Date: 3/4/2005 11:23:19 AM

> Subject: Re: [PrimeNumbers] 3+ question

>

>

> On Friday 04 March 2005 15:01, you wrote:

> > I think the below is true, but I can't prove or disprove the

> > statement. Please help.

> >

> > If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)+1)/2)

> > +1 also prime, and vice-versa? I can't find any counter examples.

> >

> > true for n=0,1,2 up to 10(Till where I checked).

>

> Law of small numbers. It's hard to tell if this is true because you can't

> check much further than that -- n = 15 is about the limit given current

> technology.

>

> Of course, for all I can tell, there could be a proof of this, but I

> be jumping to conclusions with such a small dataset.

>

> > Note:- The above terms are factors of 3^(3^(n+1))+1, hence will have

> > special factors only.

> >

> > Also, if 2*3^n+1 is prime then it divides these kind of numbers.

> >

> > I am also interested in sieving for these numbers, try to find the

> > smallest factor for each, does anyone have any software available,

> > or could write me one?

>

> I could in exchange for some CPU-time for my primo-factorial sieving and

> PRP-testing tasks (:

>

> D�cio

>

>

> [Non-text portions of this message have been removed]

>

>

>

>

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>

> - Milton Brown wrote:

> There is a Law of Small Numbers in statistics,

Googling "Law of Small Numbers" shows something in good agreement with Decio's

> but you seem to be using the term incorrectly;

> just dropping it in where it makes no sense.

use of the term, e.g.:

http://primes.utm.edu/glossary/page.php?sort=LawOfSmall

Milton's posts on the other hand, seem to often make no sense.

Harsh Aggarwal wrote:

> I think the below is true, but I can't prove or disprove the

Only true for n=0 if 1 is considered a prime. Then n = 0, 1, 2 gives 6 small

> statement. Please help.

>

> If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)+1)/2)+1

> also prime, and vice-versa? I can't find any counter examples.

>

> true for n=0,1,2 up to 10(Till where I checked).

primes: (7, 1), (37, 19), (19927, 19441).

There are no other primes for n<=10. The number of digits approximately

triples for each n. This growth is so fast that there are probably no more

primes at all. That means Harsh's guess is actually likely to be true, but in

an uninteresting way.

PS: Do not use the default primeform Fermat 3-prp test on these base 3

expressions.

--

Jens Kruse Andersen - --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"

<jens.k.a@g...>wrote:>Milton Brown wrote:

Cosigned, since the "Law of Small Numbers" makes perfect since in

>

>>There is a Law of Small Numbers in statistics,

>>but you seem to be using the term incorrectly;

>>just dropping it in where it makes no sense.

>

>Googling "Law of Small Numbers" shows something in good agreement

>with Decio's use of the term, e.g.:

>http://primes.utm.edu/glossary/page.php?sort=LawOfSmall

>

>Milton's posts on the other hand, seem to often make no sense.

this case. Looking at the first 3 tiny pairs of numbers could lead

someone to believe that there is some law "causing" this to happen.

Well, there "might" be such a law, but most likely it is due to

blind luck, and such tiny numbers which are statistically rich in

primes.

One could also look at the "plus" form, and make a statement

(although wrong), that since n=0 and n=1 and n=2 are all prime,

then all will be prime (note a Great one, Fermat made such a wild

claim in the past).

Both of the above claims are cases where the "Law of Small Numbers"

causes someone to make a false (or likely false) claim. However,

for the claim of if "plus" prime, then "minus" prime, (if the

stipulation of n>1 is added to the original question posed),

"might" be true, due to the fact that it is likely there are no

additional primes of either form. There is no "law" (that I am

aware of), but simple blind luck happened to form these pairs.

>Harsh Aggarwal wrote:

+1)/2)+1

>

>>I think the below is true, but I can't prove or disprove the

>>statement. Please help.

>>

>>If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)

>>also prime, and vice-versa? I can't find any counter examples.

gives 6

>>

>>true for n=0,1,2 up to 10(Till where I checked).

>

>Only true for n=0 if 1 is considered a prime. Then n = 0, 1, 2

>small primes: (7, 1), (37, 19), (19927, 19441).

approximately

>There are no other primes for n<=10. The number of digits

>triples for each n. This growth is so fast that there are probably

no

>more primes at all. That means Harsh's guess is actually likely to

be

>true, but in an uninteresting way.

base 3

>

>PS: Do not use the default primeform Fermat 3-prp test on these

>expressions.

I don't know about that PS statement. It might be good to have some

of the "newer" prime hunters use default Fermat-3 tests. Frequently

a wrong answer (especially one which might smack someone right in the

forehead) will help teach people willing to learn, better than a

correct answer.

>Jens Kruse Andersen

- Responding people should surely do their research before making

making such "might" be false statements:

"Well, there 'might' be such a law, but most likely it is due to

blind luck ...

Milton L. Brown

miltbrown at earthlink.net

> [Original Message]

> From: jim_fougeron <jfoug@...>

> To: <primenumbers@yahoogroups.com>

> Date: 3/5/2005 5:54:29 AM

> Subject: [PrimeNumbers] Re: 3+ question

>

>

>

> --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"

> <jens.k.a@g...>wrote:

> >Milton Brown wrote:

> >

> >>There is a Law of Small Numbers in statistics,

> >>but you seem to be using the term incorrectly;

> >>just dropping it in where it makes no sense.

> >

> >Googling "Law of Small Numbers" shows something in good agreement

> >with Decio's use of the term, e.g.:

> >http://primes.utm.edu/glossary/page.php?sort=LawOfSmall

> >

> >Milton's posts on the other hand, seem to often make no sense.

>

> Cosigned, since the "Law of Small Numbers" makes perfect since in

> this case. Looking at the first 3 tiny pairs of numbers could lead

> someone to believe that there is some law "causing" this to happen.

> Well, there "might" be such a law, but most likely it is due to

> blind luck, and such tiny numbers which are statistically rich in

> primes.

>

> One could also look at the "plus" form, and make a statement

> (although wrong), that since n=0 and n=1 and n=2 are all prime,

> then all will be prime (note a Great one, Fermat made such a wild

> claim in the past).

>

> Both of the above claims are cases where the "Law of Small Numbers"

> causes someone to make a false (or likely false) claim. However,

> for the claim of if "plus" prime, then "minus" prime, (if the

> stipulation of n>1 is added to the original question posed),

> "might" be true, due to the fact that it is likely there are no

> additional primes of either form. There is no "law" (that I am

> aware of), but simple blind luck happened to form these pairs.

>

> >Harsh Aggarwal wrote:

> >

> >>I think the below is true, but I can't prove or disprove the

> >>statement. Please help.

> >>

> >>If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)

> +1)/2)+1

> >>also prime, and vice-versa? I can't find any counter examples.

> >>

> >>true for n=0,1,2 up to 10(Till where I checked).

> >

> >Only true for n=0 if 1 is considered a prime. Then n = 0, 1, 2

> gives 6

> >small primes: (7, 1), (37, 19), (19927, 19441).

> >There are no other primes for n<=10. The number of digits

> approximately

> >triples for each n. This growth is so fast that there are probably

> no

> >more primes at all. That means Harsh's guess is actually likely to

> be

> >true, but in an uninteresting way.

> >

> >PS: Do not use the default primeform Fermat 3-prp test on these

> base 3

> >expressions.

>

> I don't know about that PS statement. It might be good to have some

> of the "newer" prime hunters use default Fermat-3 tests. Frequently

> a wrong answer (especially one which might smack someone right in the

> forehead) will help teach people willing to learn, better than a

> correct answer.

>

> >Jens Kruse Andersen

>

>

>

>

>

>

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> The Prime Pages : http://www.primepages.org/

>

>

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>

>

>

>

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