[seqfan] Re: A conjecture for double primes

Vladimir Shevelev shevelev at bgu.ac.il
Sat Apr 26 12:59:48 CEST 2014


Yesterday I have submitted a simple sequence A241536: "Smallest k>=1 such that numbers Prime(n) + or - k are both semiprimes, or a(n)=0 if there is no such k". The  behavior of the fist terms did not seem to bode special. Michel Marcus continued to calculate new terms, but starting with n=78 (prime(78)=397) and already up to n= 5*10^4 he obtained only zeros!! It is clear that large numbers have, as a rule,  more and more divisors, and one can expect that from a moment we will obtain sometimes zeros, but unexpectedly we obtained, maybe, ALL zeros.  If so, I think that it is a unique phenomenon of prime 397.

Best regards,
Vladimir

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Vladimir Shevelev [shevelev at exchange.bgu.ac.il]
Sent: 25 April 2014 17:44
To: seqfan at list.seqfan.eu
Subject: [seqfan] A conjecture for double primes

Dear Seqfans,

In new sequence A241535,  I posed a conjecture:  every even semiprime more than 22 is a sum of two semiprimes.
If for a given sufficiently large two primes p_1 and p_2  there exists a number h such that either  p_1 - h, p_2+h
or p_1 + h, p_2 - h are both semiprimes, then the conjecture essentially follows from the Goldbach binary conjecture for even numbers. Maybe, simpler, at least for sufficiently large prime p, there exists h, such that
both of numbers p-h, p+h are semiprimes.

Best regards,
Vladimir

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