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From: raycb on 15 May 2010 13:11
The primes 3, 5, 7, 11, 19, and 23 form a set in which any member can
be multiplied by any other member to produce a number that is two less
and/or two more than a prime number.

What is the next prime that can be included in this set?
From: Patrick Coilland on 15 May 2010 14:10
raycb a �crit :
> The primes 3, 5, 7, 11, 19, and 23 form a set in which any member can
> be multiplied by any other member to produce a number that is two less
> and/or two more than a prime number.
>
> What is the next prime that can be included in this set?

1657
From: James Waldby on 15 May 2010 15:00
On Sat, 15 May 2010 20:10:07 +0200, Patrick Coilland wrote:

> raycb a écrit :
>> The primes 3, 5, 7, 11, 19, and 23 form a set in which any member can
>> be multiplied by any other member to produce a number that is two less
>> and/or two more than a prime number.
>>
>> What is the next prime that can be included in this set?
>
> 1657

I agree with that, and then the next number appears to be 39727,
and then (if any) > 10^9.

Note, squares of 3, 5, 7, 19 are likewise 2 units above or
below a prime, but squares of 11, 23, 1657, 39727 are not.

--
jiw
From: Gerry Myerson on 16 May 2010 20:30
In article <hsmr08$iv5$1(a)news.eternal-september.org>,
James Waldby <no(a)no.no> wrote:

> On Sat, 15 May 2010 20:10:07 +0200, Patrick Coilland wrote:
>
> > raycb a �crit :
> >> The primes 3, 5, 7, 11, 19, and 23 form a set in which any member can
> >> be multiplied by any other member to produce a number that is two less
> >> and/or two more than a prime number.
> >>
> >> What is the next prime that can be included in this set?
> >
> > 1657
>
> I agree with that, and then the next number appears to be 39727,
> and then (if any) > 10^9.

The prime k-tuples conjecture suggests the sequence continues.
All you need is a number n such that all of these are prime:

n, 3 n + 2, 5 n + 2, 7 n + 2, 11 n + 2, 19 n + 2, 23 n + 2,
1657 n + 2, and 39727 n + 2.

--
Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
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