[seqfan] Re: On some constellations of primes

[Vladimir Shevelev]

Now this sequence is A217671. After the replacing "run" by "set" it is, evidently, monotonic. I invite colleagues to verify and continue it.

Regards,
Vladimir 



----- Original Message -----
From: Vladimir Shevelev <shevelev at bgu.ac.il>
Date: Tuesday, October 9, 2012 6:57
Subject: [seqfan] Re: On some constellations of primes
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> Thank 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).
> > 
> > 
> > _______________________________________________
> > 
> > Seqfan Mailing list - http://list.seqfan.eu/
> > 
> 
>  Shevelev Vladimir‎
> 
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> 
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> 

 Shevelev Vladimir‎