- I am not sure why you are missing my point.

But, I was not atempting to generator all twin primes,

only to use them to prove that there are an infinite number.

So, I will use whatever twins I feel like.

Perhaps you were misled by some more vocal people,

who miss the point a lot; it doesn't matter.

Don't take the liberty of modifying my material. Thank you!

The rest of you might be interested in the following table:

Least Twin Primes Past Factorial

n, n!, n+1, length, least twin primes past factorial

2 2 3 2 => (5, 7)

3 6 4 4 => (11, 13)

4 24 5 18 => (29, 31)

5 120 6 96 => (137, 139)

6 720 7 600 => (821, 823)

7 5040 8 4320 => (5099, 5101)

8 40320 9 39600 => (40427, 40429)

9 362880 10 322560 => (362951, 362953)

10 3628800 11 3265920 => (3629027, 3629029)

11 39916800 12 36288000 => (39916817, 39916819)

12 479001600 13 439084800 => (479001791, 479001793)

+(5, 7)

6+(5, 7)

24+(5, 7)

120+(17, 19) => (2*3!+5, 2*3!+7)

720+(101, 103) => (4*4!+5, 4*4!+7)

5040+(59, 61) => (2*4!+3!+5, 2*4!+3!+7)

40320+(107, 109) => (4*4!+3!+5, 4*4!+3!+7)

362880+(71, 73) => (2*4!+3*3!+5, 2*4!+3*3!+7)

3628800+(227, 229) => (5!+4*4!+3!+5, 5!+4*4!+3!+7)

39916800+(17,19) => (2*3!+5,2*3!+7)

479001600+(191,193) => (5!+2*4!+3*3!+5,5!+2*4!+3*3!+7)

2!

3!+(5,7)

4!+(5,7)

5!+2*3!+(5,7)

6!+4*4!+(5,7)

7!+2*4!+3!+(5,7)

8!+4*4!+3!+(5,7)

9!+2*4!+3*3!+(5,7)

10!+5!+4*4!+3!+(5,7)

11!+2*3!+(5,7)

12!+5!+2*4!+3*3!+(5,7)

Still seems to be quite regular here.

Milton L. Brown

> [Original Message]

> From: Mark Underwood <mark.underwood@...>

> To: <primenumbers@yahoogroups.com>

> Date: 5/6/2005 10:43:15 AM

> Subject: [PrimeNumbers] Re: Infinite Number of Twin Primes

>

>

> Jud's point is well taken. Milton's original offering was that twin

> primes would be generated from only previously generated twin primes.

>

> I took the liberty to modify Milton's original offering to this:

>

> Starting with n=3 and (5,7) as the first twin prime pair, if we add

> *or subtract* a (previously generated) twin prime pair from n! to

> generate more twin prime pairs, how far can n go before there is a

> failure to produce twins? Answer : n=22.

>

> But if instead of n! we use p#, then we can get as high as p = 61

> before there is a failure to produce. (61 is the only prime to fail

> before 103. After that failures become more common, as one might

> expect.)

>

>

> Mark

>

>

> PS to certain others: Where is the love? How can there ever be peace

> in the world if we respect our own knowledge or sensibilities or

> tradition over our fellow human beings?

>

>

>

>

>

>

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

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

>

>

> Yahoo! Groups Links

>

>

>

>

> - At 08:16 PM 5/6/2005, Milton Brown wrote:
>I am not sure why you are missing my point.

The main problem is that you haven't shown that for every n, there is an x

>But, I was not atempting to generator all twin primes,

>only to use them to prove that there are an infinite number.

>

>So, I will use whatever twins I feel like.

>Perhaps you were misled by some more vocal people,

>who miss the point a lot; it doesn't matter.

such that n!+x and n!+x+2 are both primes. It doesn't really matter if x

and x+2 are a pair of twin primes or not. Now, n!+x is more likely to be

prime for small prime x than composite x, but that is it. You haven't

shown that there must be an x that works for each n.