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Old 2020-02-08, 05:47   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
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Default 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
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Old 2020-02-10, 16:49   #2
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by MattcAnderson View Post
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?
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Old 2020-02-11, 03:43   #3
sweety439
 
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Quote:
Originally Posted by MattcAnderson View Post
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.
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Old 2020-02-11, 07:50   #4
R.D. Silverman
 
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Quote:
Originally Posted by sweety439 View Post
These are called octy primes, like the sexy primes, besides, primes separated by ten are called decy primes.
Truly profound.
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Old 2020-02-12, 07:04   #5
CRGreathouse
 
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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?
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Old 2020-02-12, 08:54   #6
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by CRGreathouse View Post
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
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Old 2020-02-13, 04:49   #7
CRGreathouse
 
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Aug 2006

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Quote:
Originally Posted by R.D. Silverman View Post
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
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