[seqfan] Re: On some constellations of primes

[Sven Simon]

There are sequences in database (A089444-A089446) with a similar property.
A089446 has two sets of 7 consecutive primes, and the floating sums of every
five consecutive primes build consecutive primes again.

2255507+2255549+2255551+2255567+2255569 = 11277743, 
2255549+2255551+2255567+2255569+2255573 = 11277809 and
2255551+2255567+2255569+2255573+2255581 = 11277841 are consecutive primes.

Just to mention if someone else finds wants to extend...

Sven

-----Ursprüngliche Nachricht-----
Von: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] Im Auftrag von Hans
Havermann
Gesendet: Dienstag, 9. Oktober 2012 15:47
An: Sequence Fanatics Discussion list
Betreff: [seqfan] Re: On some constellations of primes

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/