## Missing the Point, the Table Might Help

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• 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.
Message 1 of 2 , May 6, 2005
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@...>
> 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/
>
>
>
>
>
>
>
• ... The main problem is that you haven t shown that for every n, there is an x such that n!+x and n!+x+2 are both primes. It doesn t really matter if x and
Message 2 of 2 , May 7, 2005
At 08:16 PM 5/6/2005, Milton Brown wrote:
>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.

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