[seqfan] On some constellations of primes

Vladimir Shevelev shevelev at bgu.ac.il
Fri Oct 5 20:06:03 CEST 2012


Dear SeqFans,
 
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. This sequence is connected with two my sequences:  A166251 and A182426 (see a theorem in comment). I conjectured that there exist arbitrary long sequences of consecutive primes with such property. Reinhard Zumkeller extended A182426 up to n=10000 and after that (private communication) up to n=50000, but I did not find a term>11. Thus till now I do not know a longer sequence than the above mentioned one. Can anyone find a longer sequence or indicate
a new bound N, such that up to N such a sequence not exists.
 
Regards,
Vladimir

 Shevelev Vladimir‎



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