[QUOTE=samuel;515336]cause i have checked all combinations up to thousands power and base up to millions, that is sufficient as proof u dont need to check anything over millions
if something is right for up to million than there is no need to check after million it will always be right, common sense logic[/QUOTE]

[url]http://mathworld.wolfram.com/SkewesNumber.html[/url]
[url]https://en.wikipedia.org/wiki/Mertens_conjecture[/url]

[QUOTE=samuel;515343]ship sunk, my formula is bad thx for checking, i concede[/QUOTE]

This is a hard, but good, first step. There's a lot of math out there to learn, and we're not built to learn it. We need to shape our intuition for it. You can do it -- you can do great -- if you put your mind to it. :smile:

[QUOTE=samuel;515343]ship sunk, my formula is bad thx for checking, i concede


i cry =(((((((([/QUOTE]

How about sharing your blessed formula with us now that it has been shown to be unsuccessful :huh:

[QUOTE=samuel;515336]cause i have checked all combinations up to thousands power and base up to millions, that is sufficient as proof u dont need to check anything over millions
if something is right for up to million than there is no need to check after million it will always be right, common sense logic[/QUOTE]

Your common sense is terrible. There are many outcomes in number theory whose first instance is over a million (or over the one-millionth power of an integer above 1).

For instance, 124125*6^n + 1 is not prime for any n below 1 million. By your logic, there is no need to check for any more primes, "not prime" will always be right.
However, it is prime for 124125*6^2018254+1.

[QUOTE=VBCurtis;515348]Your common sense is terrible. There are many outcomes in number theory whose first instance is over a million (or over the one-millionth power of an integer above 1).[/QUOTE]

But that's just the thing -- none of us come wired for number theory. We have to build an intuition for it. You already have, so the moment you read that you knew it was questionable. (Me too.) But our young friend hasn't had the chance to gain that same experience, and that's why I left him links explaining two cases where large counterexamples have been found to number-theoretic conjectures. You gave another example. Maybe after seeing enough examples samuel will gain the same sort of intuition we have.

[QUOTE=CRGreathouse;515349]But that's just the thing -- none of us come wired for number theory. We have to build an intuition for it. You already have, so the moment you read that you knew it was questionable. (Me too.) But our young friend hasn't had the chance to gain that same experience, and that's why I left him links explaining two cases where large counterexamples have been found to number-theoretic conjectures. You gave another example. Maybe after seeing enough examples samuel will gain the same sort of intuition we have.[/QUOTE]

There's a truly excellent book about maths mistakes called Humble Pi by Matt Parker. He talks a lot about how our human brain is wired for survival from an evolutionary perspective - to believe that if the lion is friendly to us a million times, it isn't a predator. This of course doesn't stop the lion attacking on the 1000001st visit. Number theory is illogical to the way our brains have evolved and requires a lot of reprogramming. I reccomend the book wholeheartedly, it's a popular science book so it's very accessible.

[QUOTE=chalsall;515341]There is a truism... Nature abhors a vacuum.[/QUOTE]Hence the existence of zero point energy.

[QUOTE=CRGreathouse;515349]But that's just the thing -- none of us come wired for number theory. [/QUOTE]

Here is a classic counterexample to that:


[url]https://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/The-Story-of-Gauss/[/url]

In fact there are people (many autistic) with intuitive lightening-calculation capabilities.
I doubt very much that Euler could have studied a great deal on the subject matters that he originated.

[QUOTE=a1call;515383]Here is a classic counterexample to that:


[url]https://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/The-Story-of-Gauss/[/url][/QUOTE]

And where did Gauss learn his arithmetic? By studying what he saw his father write and do -- he was an accountant. His everyday life revolved around summing numbers, and so it's really no surprise that by the time he got to school he was vastly more prepared than other students for an addition challenge. (But no doubt children with parents who were diplomats were more prepared for diplomatic challenges, and so forth.)

:smile:

[QUOTE=dcheuk;515142]Just an update, 1 day 20 hours left for [M]88680457[/M] on CUDALucas!

This might be embarrassing but at first this doesn't look that bad, but then I spent an hour attempting to prove it using analysis and ring theory but to no avail. I should probably go back to learning number theory ... :picard:[/QUOTE]

Update: LL test completed and confirmed composite.

The formula
 

May we please see the formula?