Value for Brun's constant below vs. OEIS value (A065421) is 1.9021605831029730799822614917... 1.902160583104 If the OEIS value is a lower bound then the conjectured formula is incorrect. Best regards, jj * rcs@xmission.com <rcs@xmission.com> [Aug 06. 2018 08:40]:
Gentlemen, start your engines. --Rich
----- Forwarded message from lesniakowie@GMAIL.COM ----- Date: Mon, 30 Jul 2018 14:16:40 -0500 From: Marcin Le?niak <lesniakowie@GMAIL.COM> Reply-To: Number Theory List <NMBRTHRY@LISTSERV.NODAK.EDU>, Marcin Le?niak <lesniakowie@GMAIL.COM> Subject: Possible relation between Catalan?s, Ramanujan-Soldner?s and Brun?s constants To: NMBRTHRY@LISTSERV.NODAK.EDU
Hello everybody,
I'm new to this list and was advised (by one of the members) to share here my conjecture of a possible relation between the three constants related generally with the distribution of primes. The relation is completely surprising and unexpected (neither I nor two experts in number theory couldn't find the reason for its existence) but amazingly simple, and this is why I believe could be real...
Conjecture concerns the relation between Catalanâs, Ramanujan-Soldnerâs and Brunâs constants resulting in receiving the closed formula for Brun's constant, which direct computation is not possible so far and is based on extrapolation of achievable computational results made with the help of the twin primes conjecture.
Let G be the Catalanâs constant, equal to β(2) (Dirichlet beta function for s=2) G = β(2) = 0.91596559417721901505460351493238411077414937â¦
Let µ be the Ramanujan-Soldner constant µ = 1.45136923488338105028396848589202744949303228â¦
Let B2 be the Brunâs constant
Conjecture: B2= (8+40(µ-G))/(16-(µ-G)) = 1.9021605831029730799822614917574361â¦
As I said this relation is so surprising, that Iâd like to encourage you all to help find its explanation - maybe it could shed the new light on the problem of distribution of the twin (and other constellations) primes.
I'm very curious about your opinion about it :-)
Kind regards, Marcin LeÅniak
----- End forwarded message -----
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun