- Mar 1, 2005--- In primenumbers@yahoogroups.com, Chris Caldwell <caldwell@u...>

wrote:> At 01:43 PM 2/27/2005, Décio Luiz Gazzoni Filho wrote:

problem

> >> 2. Why do people choose to broadcast their solutions to this

> >> on the internet?

chance in hell

> >

> >Beats me. But it makes no difference, because anyone who had a

>

that will eventually be in reputable journals is first circulated by

> Depends what you mean by broadcast. Virtually all mathematics

preprint; often on the Internet. Mathematicians often say if you

are waiting to read journals then you are two-years behind the

current research.> Example: "Primes in P" was circulated on the net, gained

acceptance,

> was improved on repeatedly, all well before its first publication.

corrections

>

> You circulate in any media to share what you have. Often you get

> and suggestions. Sometimes references that you missed. (Amateurs

I do hate to being called a crackpot by people who DON'T think what

> often miss the point of references--you must show you know how your

> works fits in with the current literature.)

>

> But if instead you mean why do they have "Goldbach Proof" websites.

> That is because no one would publish their trash. Audience is the

> key--who are you writing to?

Chris is saying here is a good way to gain acceptance. I just wish

there where more people who could help me when I have questions and

willing to help me find the answers. For example I have recieved the

following fowarded message which I can not answer. I wonder if any

of you can. If not who and where can I ask?

Can you answer the following?

John

---------

From: John W. Nicholson <reddwarf2956@...>

To: caldwell@...

Subject: Questions

Sent: Friday, January 28, 2005 7:24 PM

I have many question. ;-)

On your page with Fortunate numbers:

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

Is there a term for prime numbers not in both Fortunate number and

the

Fortunate number list? I am thinking of calling them unfortunate

prime numbers.

Simular, but for primes that show up more than once, like 61 called

very

fortunate numbers. Are there an infinete number of both types?

Is there a relationship between composite pair of p#+/-1 and the

size of the

gap mentioned? With both of these numbers composite there is a large

gap

between the less Fortunate number and the Fortunate number. How big

is it?

I know there is a relationship between the gap with p#+/-1 and the p!

+/-1 gap.

I mean if p#+/-1 is prime, then there is a gap >= the gap of size p.

Because p!

has a gap after p!+1 of at least p, realize that n!/n# = integer.

And For any N, the sequence (N + 1)! + 2, (N + 1)! + 3, ..., (N +

1)! + N + 1

the gap is of size n.

From: Paulo Ribenboim's book The Little Book of Big Primes. page 142

In your paper on http://primes.utm.edu/references/refs.cgi?

long=CG2000 states

some proofs, namely theorems 2.4 and 2.5, which relates to p# or

some number <

p#, right? I mean there is a prime q which has the same congruences

to p! as to

p#.

Can you state theorems 2.4 and 2.5 on web pages connected

with "factorial

primes"? You might want to link the primorial prime pages to it to

the

Fortunate numbers?

Also, you might add to the page

http://primes.utm.edu/glossary/page.php?sort=PrimeGaps a comment

about the gap

stated above. I know that it is not the smallest gap because 89 is

the first

the gap which follows the sum of two gaps larger than the n! gap.

With "sum of

two gaps" I mean while looking at largest number of the smallest

factor of

composites of the gap. This may sound confusing, so restating.

For a gap, d, for a prime number p_n to p_(n+1), there are d numbers

which are

composite to primes smaller than p_n and p_(n+1). Each of these

composites have

a factor f_d which is the smallest factor. The largest f_d in the

gap makes the

final gap size d by summing the gap that was before and after. This

was for the

d after p_n there is another one for d before p_n too. Is there a

previously

stated gap function with these terms? If not, why not?

More questions with http://primes.utm.edu/references/refs.cgi?

long=CG2000

In Theorem 2.4 is

i) n divides 1!-1 and 0!-1

Why is this statement needed? I mean (1!-1)/n = 0 and (0!-1)/n = 0,

right?

Table 4:

1) What reason are the other primes < 499 not listed?

2) Why are there pairs? (My guess is that there is a relationship

with

quadratic congruences.)

3) Is there a proof which states that the individual pairing (the

ones in

which p = n - k -1) is always even-even or odd-odd but the total

pairing does

not have to be all even or all odd? Why are they not mixed?

4) With my guess with quadratic congruences, what is relationship

of the signs

of the units added with quadratic congruences?

5) No squares with pairings. Why? Also no n^m? Why, again?

6) Is there a correlation between the factor and the sign of the

unit?

7) Is there a correlation between the factorial and the sign of the

unit?

8) Is there a correlation between the k value and the sign of the

unit?

9) Are there tables of factors of factorial numbers n!+/-1

somewhere? (at

least to 4000, to get pass the Wilson and Wieferich primes 563,

1093, and 3511,

with and without the pairing)

10) With twins, how does the above questions relate?

11) I see with 16!+1 both 137 and 139 are factors, does this mean

anything with

twins? What about 16!+1 pairs 120!-1 and 122!-1?

12) I see with prime 61 both 16!+1 and 18!+1 are divisible

factorials, does

this mean anything with twins? Again, with the factorial pairs

respectfully?

13) What about with: Theorem: (Clement 1949)

The integers n, n+2, form a pair of twin primes if and only if

4[(n-1)!+1] = -n (mod n(n+2))?

How about with this theorem with the theorems 2.4 and 2.5 and the

one here

http://www.primepuzzles.net/problems/prob_002.htm?

From your page: http://primes.utm.edu/glossary/page.php?

sort=TwinPrime and the

book stated above too.

14) What about Wilson primes, is there anything relating them to

(mod n^2)?

Can the theorem state in Q13) be combined with Proth's? Maybe some

other prime test, like Fermat's little theorem or a strong psp test?

Can you make a web page on the inclusion/exclusion principle

relitive to primes? You could show why all attempts so far with the

twin primes conjecture has failed. - << Previous post in topic