>Well, 10 is representable as kp+10 when k=0 and p=59 or p=61 but I

>guess you mean for k>0.

Yes I did.

Jon Perry

perry@...
http://www.users.globalnet.co.uk/~perry/maths
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-----Original Message-----

From: richard_heylen [mailto:

richard_heylen@...]

Sent: 17 April 2002 00:01

To:

primenumbers@yahoogroups.com
Subject: [PrimeNumbers] Re: Twin Primes Waffle

--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

> Can anyone prove that only using all the primes 5 and above, there

are an

> infinite number of integers not representable by:

>

> kp+/-j, where j is such that p=6j+/-1.

>

> e.g. 10 is not 5k+/-1, or 7k+/-1, or 11k+/-2 or 13k+/-2

>

> whereas 9 is both 5-1 and 11-2.

>

> 10 not being present implies that 59 and 61 are twin primes.

Well, 10 is representable as kp+10 when k=0 and p=59 or p=61 but I

guess you mean for k>0.

As for whether there are an infinite number of non-representable

integers, it is indeed equivalent to the twin primes conjecture as

you suggest.

Richard

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