[seqfan] Re: On some constellations of primes

[zak seidov]

",,,I hope that you (or you and Zak) can submit this 
sequence." 

Sorry,  somehow I've lost thread (& interest) in the subject 
& readily abstain from submitting this particular sequence.
Regards, 
Zak  



----- Original Message -----
> From: Vladimir Shevelev <shevelev at bgu.ac.il>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Cc: 
> Sent: Tuesday, October 9, 2012 9:29 PM
> Subject: [seqfan] Re: On some constellations of primes
> 
>T hank you, Hans, for this right and important remark. Such sets of consecutive 
> primes are connected with the isolated primes (A166251). It is based on 
> Propositions 13 and 16 of my paper in link. These propositions
> forbid to the interior primes of such a sequence to be non-isolated, but allow 
> to the first prime to be only "isolated from the right", while to the 
> last prime to be only "isolated from the left"
> (or, by my classification, the first prime can be "left prime", while  
> the last prime can be "right prime").  Therefore, in the constructing 
> the suggested
> sequence we need to verify one prime before a run of consecutive isolated primes 
> and one prime after it. I hope that you (or you and Zak) can submit this 
> sequence. 
> 
> Best,
> Vladimir
> 
> 
> ----- Original Message -----
> From: Hans Havermann <gladhobo at teksavvy.com>
> Date: Tuesday, October 9, 2012 1:46
> Subject: [seqfan] Re: On some constellations of primes
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> 
>>  Vladimir Shevelev:
>> 
>>  > The following sequence of 11 consecutive primes
>>  > 55469,55487,55501,55511,55529,55541,55547,55579,55589,55603,55609
>>  > possesses an interesting property: between every adjacent half-
>> 
>>  > primes there exists at least one prime. In particular, between 
>>  the  
>>  > first two half-primes there are 3 primes: 27737,27739,27743.
>> 
>> 
>>  The prime previous to 55469 is 55457. Between 55457/2 and 
>>  55469/2 is  
>>  the prime 27733.
>>  The prime after 55609 is 55619. Between 55609/2 and 55619/2 is 
>>  the  
>>  prime 27809.
>> 
>>  I don't understand why the two either-end consecutive primes are 
>>  being  
>>  excluded here. This appears to be so as well for Vladimir's 
>>  follow-up  
>>  "a(2)=5, a(3)=79, a(4)=541, a(5)=6599, a(6)=10771".
>> 
>> 
>>  Zak Seidov:
>> 
>>  > Smallest set of 13 (VladSh's) consecutive primes:
>>  > s=prime(1785277..1785289)={28751809, 28751851, 28751857, 
>>  28751873,  
>>  > 28751893, 28751903, 28751929, 28751941, 28751969, 
>>  28751977,  
>>  > 28752007, 28752019, 28752037},
>>  > 12 corresponding smallest primes q(k) between (1/2)s(k) and 
>>  (1/2)s(k 
>>  > +1):
>>  > q(k=1..12)={14375923, 14375927, 14375929, 14375939, 
>>  14375947,  
>>  > 14375957,
>>  >  14375969, 14375981, 14375987, 14376001, 14376007, 14376013};
>> 
>>  The prime previous to 28751809 is 28751773. Between 28751773/2 
>>  and  
>>  28751809/2 is the prime 14375899.
>>  I'm going to guess that Zak's program searched for 13 intervals 
>>  (i.e.,  
>>  14 consecutive primes).
>> 
>> 
>>  _______________________________________________
>> 
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>> 
> 
> Shevelev Vladimir‎
> 
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