C1.

@RRL I couldn't find D17 to D19, but the rest are gone.

@user21820: Thank you very much. That was a typo -- I only listed D1 - D16. Sorry.

@Randall Normally, you just flag. But next time you can also just post the links here and we can look at them.

C1, C2.

@XanderHenderson @RRL @rschwieb @TheSimpliFire: Wrong answer has 4 upvotes and tick despite @JoséCarlosSantos pointing out the flaw.

And why is this same user asking PSQs about point set topology when they produce nonsense response to very basic middle school questions??

More PSQs here and here.

Another example of blind copy-paste of mathematical expressions. Sometimes I can't believe what passes for effort.

C3, C4, C5.

C6, C7, C8.

Another PSQ to close.

C9, C10, C11.

D1, D2, D3.

D4, D5, D6.

D7, D8.

D9, D10, D11, D12.

It is not the accepted answer anymore and therefore it will be easier to delete.

@user21820 Why do you want to close the questions C9, C10, and C11? I think that they are interesting and that who asked them provided enough context.

PSQ for closure.

@JoséCarlosSantos C9 seems to be asking "Hey, I saw this pattern and have never heard of the law of small numbers. 'Sup with that?"

It is poorly researched, hence I don't think that it is worth keeping around. The only non-deleted answer at the moment is "You didn't do enough work. Compute more terms. Your pattern fails." I don't see the value of that.

For C10, I am not sure that I see what the question actually is. The wall of links is also difficult to get through. The last sentence, however, seems to indicate that the asker is looking for generalizations for several conjectures or results? This seems overly broad.

C11 took me a while to parse (I don't think that it is very clearly written). However, at the end of the day, I think it is bordering on numerology. There is not enough context there to explain why I should care about the greatest prime factor of the sum of the first $n$ primes, nor do I understand what is interesting about the "pattern" noted by the asker.

@XanderHenderson Why in the world would you think that C9 has anything to do with numerology? In fact much of number theory (and algebra) was motivated by analogous numerical observations. Experimental number theory is not numerology.

@BillDubuque I did not assert that C9 was numerology.

Upvoted PSQ with multiple answers

@XanderHenderson What is your definition of "numerology"?

@BillDubuque My comments above are, I think, quite clear.

@XanderHenderson If you don''t define "numerology" then your comment is meaningless

@BillDubuque You mean the nonexistent comment in which I linked C9 to numerology, or the actual comment regarding C11 where, over the course of three sentences, I laid out a case for closing that question on the grounds that it was unclear, but also made an offhand and well-hedged comment about it being "bordering on numerology"?

@XanderHenderson You certainly used the word "numerology". If you can't explain what that means then your comment has about the same value as "numerology" (whatever it means)

@BillDubuque I do not claim that I did not use the word "numerology". in fact, if you were to reread what I just wrote, you would see that I used that word in association with the hedge "bordering on" as a description of C11.

@XanderHenderson So you use highly loaded words to denigrate mathematical questions but you can't explain what they mean?

@BillDubuque I am disengaging now. Long experience has shown that conversations with you tend to be unproductive. I think that my comments were clear. You are free to give them whatever value you think they deserve, and act as you see fit. You may have the last word, if you like. Good day.

@XanderHenderson Just as I surmised - you are unable to give any reasonable definition of "numerology" to support your claim. In my opinion, unsound arguments like that are far more harmful than what some deem as "numerology".

Maybe I should explain why this bothers me so much. If one studies the history of math one can find all sorts of analogous harmful denigrations. For example, Joseph Ritt, a founder of differential algebra, though p-adics were useless and called them "monkey fields" But as we know nowadays they are quite useful (even in Diff. Algebra, as his student Kolchin showed).

It is difficult if not impossible even for experts to predict whether or not some ideas will ever prove fruitful. So it is generally foolish to make guesses about such. One shouldn't vote to close questions simply because you are not interested in certain mathematical topics.

@user525966 I would be slightly more encompassing in the way that I understand the word: numerology is the search for significance or meaning in numbers. The question that I called "borderline numerology" asserts that there is a pattern (without much evidence) then asks to know if the pattern is real or not. My principle objections to the question are that it is unclear and lacking context.

However, I think that the assertion that the pattern is meaningful or significant (with no justification given) does border on numerology. It ascribes meaning to a pseudo-pattern in a nebulous way; this is the same kind of thing that kabbalahists do (though not to the same degree).

@XanderHenderson Do you consider ancient conjectures on nonexistence of odd perfect numbers to be numerology? What is a "pseudo-pattern"?

Btw, I don't recall where I first heard about Ritt, but a search shows an analogous remark by one of his students, see p. xiii of Kolchin's Differential Algebra & Algebraic Groups where he writes 'Ritt himself had no use for fields of nonzero characteristic and referred to them as "monkey fields"'.

Alas, there are many analogous examples throughout the history of mathematics.

@XanderHenderson To counter: One classic example is how one might notice that the number of moves involved in the Tower of Hanoi problem is 1, 3, 7, 15, 31, ... which looks like a pattern 2^n-1, but maybe you can't compute the next value to see if the pattern holds because the game starts to take too long. You don't actually know if it's a pattern, or if your pattern even holds. (And then someone can answer, "It actually does hold and you can prove it with induction..." and so forth).

Whether or not a pattern ends up existing or being useful, in my opinion, is something we can only really figure out by asking the question, looking for an answer, and seeing over time how the result ends up being used

I agree though that the post is unclear and lacks context... hard to tell what's being asked

He appears to be asking how many values satisfy largestPrimeFactor(primeSum(n)) = the {(n+1)/2}nd prime but for so few values I am unsure how he came about this question or why he's asking it. So I agree with your conclusion, I just wouldn't call it "borderline numerology" which is a fairly charged term.

On 2nd thought I think I heard about Ritt from a conversation with Rota. Which reminds me of a related one of his "indiscrete thoughts". In the old days many analysts also thought proofs using formal power series were meaningless numerology. Believe it or not such misunderstanding can even exist here and now, e.g. see this thread, where a (now deleted) answer got many upvotes before a correct answer was posted.

Nowadays I suspect one needs to know more algebra to do anaylsis, so there is less chance for such oversights.

@user525966 But in this problem, there is an actual underlying game or mechanism which one wants to understand. The search for a pattern is motivated. In the case of C11, the asker asserts the existence of a pattern without motivation or context. To me, this looks like an example of the "law of small numbers" and reflects the human tendency to see patterns (humans are wired by evolution to see patterns, even if they aren't there).

It is because of this over-matching and unmotivated pattern finding that I think that the question borders on the numerological.

In any event, that was only a small part of my objection to the question. The lack of clarity and context are far more pressing issues.

@XanderHenderson Please study the history of math. If you do so you'll learn that much of number theory and algebra was discovered this way.

That being said, if the only objection is the use of a single word, I am happy to rephrase:

> C11 took me a while to parse (I don't think that it is very clearly written). However, at the end of the day, I think it is the result of seeing patterns where there are none. There is not enough context there to explain why I should care about the greatest prime factor of the sum of the first n primes, nor do I understand what is interesting about the "pattern" noted by the asker.

@XanderHenderson I'd agree with that rephrasing

psq math.stackexchange.com/q/3120367/29335

delete 1, 2, 3, 4

@rschwieb That PSQ is closed now and you can already vote to delete it.

reopen? – This question was closed as a duplicate of this older question. However, the newer question asks for less (determine p'(0) from a functional equation), whereas the older question asks for the general solution of that equation. OP also asks for a more “elementary” solution of this reduced problem.

I do not know if a simple solution to the simpler question exist (at least one comment indicates it), but I would suggest to reopen the question.

delete 5, 6, 7, 8

@JoséCarlosSantos Why are you analyzing and deleting 5-year-old questions? Is it merely a coincidence that 75% of those questions contain highly-voted answers by a high-rep user (currently suspended).