primes separated by eight

[MattcAnderson]

Hi Mersenneforum and all,

Contributed to Encyclopedia -

see link to Online Encyclopedia of Integer Sequences

Regards,

Matt

[R.D. Silverman]

Originally Posted by MattcAnderson

Hi Mersenneforum and all,

Contributed to Encyclopedia -

see link to Online Encyclopedia of Integer Sequences

Regards,

Matt

This particular subforum is supposed to be for the discussion of mathematics.

I see no mathematics discussed here. I do 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 welcome it.

Otherwise, please take your trivial computations 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?

[sweety439]

Originally Posted by MattcAnderson

Hi Mersenneforum and all,

Contributed to Encyclopedia -

see link to Online Encyclopedia of Integer Sequences

Regards,

Matt

These are called octy primes, like the sexy primes, besides, primes separated by ten are called decy primes.

[R.D. Silverman]

Originally Posted by sweety439

These are called octy primes, like the sexy primes, besides, primes separated by ten are called decy primes.

Truly profound.

[CRGreathouse]

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:

• 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?

[R.D. Silverman]

Originally Posted by CRGreathouse

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.

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.

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

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

http://michaelnielsen.org/polymath1/...between_primes


Or any math at all 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.

[CRGreathouse]

Originally Posted by R.D. Silverman

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.

Let's!

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