primes separated by eight
 

Hi Mersenneforum and all,

Contributed to Encyclopedia -

see [URL="oeis.org/A023202"]link to Online Encyclopedia of Integer Sequences[/URL]

Regards,

Matt

[QUOTE=MattcAnderson;537051]Hi Mersenneforum and all,

Contributed to Encyclopedia -

see [URL="oeis.org/A023202"]link to Online Encyclopedia of Integer Sequences[/URL]

Regards,

Matt[/QUOTE]

This particular subforum is [i]supposed[/i] to be for the discussion of mathematics.

I see no mathematics discussed here. I [b]do[/b] see some mindless numerology.

The mathematics behind Schinzel's conjecture and the Bateman-Horn conjecture
is well known, although a formal proof is lacking. If you would like to discuss
the attempts to prove these conjectures, I [b]welcome[/b] it.

Otherwise, please take your trivial [i]computations[/i] somewhere else. I am surprised
that anyone would have the arrogance to submit such a trivial, well-known sequence
to the on-line encyclopedia. I certainly would not do it under my own name. Are
you that hard-up for recognition?

[QUOTE=MattcAnderson;537051]Hi Mersenneforum and all,

Contributed to Encyclopedia -

see [URL="oeis.org/A023202"]link to Online Encyclopedia of Integer Sequences[/URL]

Regards,

Matt[/QUOTE]

These are called [B][I]octy primes[/I][/B], like the sexy primes, besides, primes separated by ten are called decy primes.

[QUOTE=sweety439;537295]These are called [B][I]octy primes[/I][/B], like the sexy primes, besides, primes separated by ten are called decy primes.[/QUOTE]

Truly profound.

Thank you, Matt, for your contribution. I do prefer to see existing sequences enriched than to see new, less-obviously-interesting sequences submitted. And fortunately this sequence has a number of mathematical features that should keep Silverman awake.

If you would like to appease him, I might suggest looking into some of its deeper features. To wit:[list][*] Granville & Martin are cited here. Could you see how their "prime number races" apply to this sequence? What other sequences might they race? Do they appear to be winning or losing?[*] A paper of Maxie D. Schmidt is cited. I haven't read it; does it cite this sequence in particular? Can be be applied to this sequence? Could you add a comment along the lines of "Schmidt proves that a(n) is congruent to ..."? These comments are useful and very much welcome in the Encyclopedia![*] For something simpler, look at the cross-references, where it says: "Disjoint union of A007530, A031926, A049437, A049438." Can you prove that this is true? (It is, up to initial first terms I haven't bothered to check.) Could you build other nice unions from the remaining cross-references?[*] Is there something else that could be transformed or cited or otherwise looked at differently?[/list]

[QUOTE=CRGreathouse;537405]Thank you, Matt, for your contribution. I do prefer to see existing sequences enriched than to see new, less-obviously-interesting sequences submitted. And fortunately this sequence has a number of mathematical features that should keep Silverman awake.
[/QUOTE]

Absolutely. Let's discuss some actual math, rather than just doing blind computation.

Let's also discuss how the parity problem prevents a formal proof based on
sieve methods. Or the related problems of how limitations applied to showing that Lambda(N) * Lambda(N+8)
can be used to form a Dirichlet series also fail to prove the result [at least, so far] . Or how Terry Tao's
analysis on Hardy-Littlewood is relevant.

[ [url]https://terrytao.wordpress.com/page/1/][/url]

Or what is needed to reduce the
bound found by the work of the Zhang, Maynard, and Tao:

[url]http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes[/url]


Or [i]any math at all[/i] that is relevant. I am simply bemoaning the fact that in a sub-forum that is supposedly
devoted to math [esp. number theory], we never see any.

This doesn't need to be a research level discussion. But I never even saw a single
post discussing the Zhang/Tao/.Maynard results. Or even a discussion of the
Bateman-Horn conjecture itself. All we see is blind computation.

Part of the problem, of course, are the limitations of this medium. Formatting
TeX can be a cumbersome process.

[QUOTE=R.D. Silverman;537412]Absolutely. Let's discuss some actual math, rather than just doing blind computation.

Let's also discuss how the parity problem prevents a formal proof based on
sieve methods. Or the related problems of how limitations applied to showing that Lambda(N) * Lambda(N+8)
can be used to form a Dirichlet series also fail to prove the result [at least, so far] . Or how Terry Tao's
analysis on Hardy-Littlewood is relevant. [/QUOTE]

Let's!

I made a thread here, please add your expertise as appropriate.
[url]https://mersenneforum.org/showthread.php?p=537469[/url]