- Perhaps a computer search would be better for you.

Or, see the link http://primes.utm.edu/lists/small/1ktwins.txt

(7!+59, 7!+61) = (5099, 5101) is a prime pair.

Milton L. Brown

> [Original Message]

twins

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

> To: <primenumbers@yahoogroups.com>

> Date: 5/5/2005 4:14:35 PM

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

>

> On Thursday 05 May 2005 19:49, you wrote:

> > At 04:54 PM 5/5/2005, Milton Brown wrote:

> > >This is the pattern: Start at the next factorial and add prior pairs of

> > >twin primes,

> > >until you obtain a pair of twin primes for that factorial.

> >

> > How do you know that will work (that you will always obtain a pair of

> > for that factorial)?

need a

>

> The answer is, he doesn't, because it won't work. This one didn't even

> computer search; it fell to a search by hand. I would appreciate a third

adds

> check (I've already double-checked locally).

>

> Start from (3,5).

>

> 2!+3, 2!+5 adds (5,7). Values found until now: (3,5), (5,7).

>

> 3!+5, 3!+7 adds (11,13). 3!+11, 3!+13 adds (17,19).

> Values found until now: (3,5), (5,7), (11,13), (17,19).

>

> 4!+5, 4!+7 adds (29,31). 4!+17, 4!+19 adds (41,43).

> Values found until now: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43).

>

> 5!+17, 5!+19 adds (137,139). 5!+29, 5!+31 adds (149,151). 5!+149, 5!+151

> (269,271).

> Values found until now: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43),

> (137,139), (149,151), (269,271).

>

> 6!+137, 6!+139 adds (857,859).

> Values found until now: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43),

> (137,139), (149,151), (269,271), (857,859).

>

> Finally, 7! doesn't produce any values. And thus Milton's conjecture is

> demolished, as about anything that he brainfarts on this list.

>

> D�cio

>

>

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

>

>

>

>

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>

>

>

> - 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?