# [seqfan] Re: Primes and prime sums

Jack Brennen jfb at brennen.net
Mon Jan 14 22:31:10 CET 2013

```It won't.  If you have p,4,q in the sequence, that would mean that:

p, q, p+4, and q+4 are all prime.

Assuming p>3, if q = p+2, then p+4 is divisible by 3.
Assuming p>3, if q = p+4, then q+4 is divisible by 3.
Assuming p>3, if q > p+4, then p+4 is not prime.

On 1/14/2013 1:18 PM, Maximilian Hasler wrote:
> Can anyone find the index at which will appear the number 4?
>
> Maximilian
>
>
> On Mon, Jan 14, 2013 at 1:19 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>> Hello Seq-Fans,
>>
>> Write down the prime numbers:
>> 2, 3, 5, 7, 11, 13, 17, 19, 23, ...
>>
>> Insert between two primes the
>> smallest integer not yet present
>> in the sequence such that two
>> neighboring integers sum up to
>> a prime.
>>
>> I think the sequence starts:
>> 2,0,3,8,5,6,7,12,11,18,13,26,17,...
>> Best,
>> É.
>>
>>
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>>
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>
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```