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 2020-02-08, 05:47 #1 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 22×149 Posts primes separated by eight Hi Mersenneforum and all, Contributed to Encyclopedia - see link to Online Encyclopedia of Integer Sequences Regards, Matt Last fiddled with by MattcAnderson on 2020-02-08 at 05:48 Reason: added link
2020-02-10, 16:49   #2
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 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.

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?

2020-02-11, 03:43   #3
sweety439

Nov 2016

13·173 Posts

Quote:
 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.

2020-02-11, 07:50   #4
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by sweety439 These are called octy primes, like the sexy primes, besides, primes separated by ten are called decy primes.
Truly profound.

 2020-02-12, 07:04 #5 CRGreathouse     Aug 2006 3·52·79 Posts 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?
2020-02-12, 08:54   #6
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 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.

Last fiddled with by R.D. Silverman on 2020-02-12 at 08:55 Reason: pagination

2020-02-13, 04:49   #7
CRGreathouse

Aug 2006

3×52×79 Posts

Quote:
 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!

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