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8 hours ago, Tinacity said:

Does the silence mean I goofed up on my whole narrative too many times?

Or discomfort with the implication that I am withholding my main project? That isn't a matter of disrespect......Just protecting a LOT of work.

Or do community members feel that my fifteen minutes of attention are up?

Or is it that I simply make no sense, still?

Or that my presentation style is just too casual, prosaic and/or inaccurate.

Or is it boredom.....lol !!?

A few weeks ago I had the problem space mapped into my brain for an evening. Too busy to remap it at the moment, so probably won't be able to get back to this. Off the top of my head I don't think the totient function will always give the same answer as inclusion/exclusion, but I could be wrong and probably am. Sorry I can't offer more assistance.

 

 

Edited by wtf
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Now that I think about it, the product of the first 23 is, as you say, 223092870. Now, the number of ways in which you can sum two (arbitrary) natural numbers to give N is just 111'546'435, becau

I did look at this one, but I am sorry to say that all of us have parts of our subject we like more than other parts. And  amongst my personally least liked parts are combinatoric and number theory.

The point is that  prime no prime number greater than 23 is divisible by any of the first 9 primes. So each prime number and its pair which adds to make  223092870 will be candidates for inclusio

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@wtf

 

Thank you for your inputs thus far. 

I am not sure why it is important for "the totient function will always give the same answer as inclusion/exclusion" unless one of the two (or both) gives an inaccurate answer in some cases. Are you arguing that?

 

Reviewing my work on the assumption I wanted to make about (3-2)(5-2)(7-2).......(p-2)................I am pretty satisified that this is a perfectly accurate way to calculate the number of relative prime pairs as argued by me so far.......I had simply forgotten that I had proven this to myself.

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9 hours ago, Tinacity said:

I am not sure why it is important for "the totient function will always give the same answer as inclusion/exclusion" unless one of the two (or both) gives an inaccurate answer in some cases. Are you arguing that?

If they give different answers then clearly at least one (or possibly both) are inaccurate. But my statement is just a guess and not based on thinking about the problem much.

 

 

9 hours ago, Tinacity said:

Reviewing my work on the assumption I wanted to make about (3-2)(5-2)(7-2).......(p-2)................I am pretty satisified that this is a perfectly accurate way to calculate the number of relative prime pairs as argued by me so far.......I had simply forgotten that I had proven this to myself.

You're probably right.

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7 hours ago, Tinacity said:

I hadn't noticed yet that they were giving different answers in the examples used. 

I think you're right that inclusion-exclusion and Euler totient give the same result for your problem. 

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9 hours ago, Tinacity said:

Do you envisage or presume a case where Euler's totient would be imprecise @wtf  and inclusion/exclusion would be more precise?

I have not given this any detailed thought since weeks ago and, to the minimal extent I've thought about this recently, I agree that you're right. The totient function gives the same answer as the inclusion/exclusion principle for this problem.

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22 minutes ago, Tinacity said:

Any idea @wtf , why this post has received the third highest number of views on this part of the forum?

image.thumb.png.df14cc39df769a67f44c256a5ade2c79.pngthis topic has

Probably because the title has 3 words that may appear easily in a search (Firts, Post, Prime). It may even happen that some viewers are bots.

See here

 

Edited by michel123456
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22 hours ago, Tinacity said:

And you feel this would account for such a large number of "views" within two months of a post?

 

@michel123456

You asked for an idea. Since WhosTheFool (wtf) did not answer, I couldn't resist the temptation to drop my idea. What is your's?

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On 1/1/2021 at 4:39 AM, michel123456 said:

It may even happen that some viewers are bots.

 

Darn, I'm busted. 

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4 hours ago, michel123456 said:

You asked for an idea. Since WhosTheFool (wtf) did not answer, I couldn't resist the temptation to drop my idea. What is your's?

I assure you that I wasn't being sarcastic when I replied to you.....and I do thank you for your input.

I just feel that it seemed unlikely to me, though a good potential explanation.....Unlikely; considering the age of the post and that looking down the list of posts sorted by view number.....that kind of aberration seemed less likely due to the other posts looking unaffected by those kind of issues. 

I can't think of any "good" explanation as yet..

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