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-   -   A prime number "game of life": can floor(y*p#) always be prime? (https://www.mersenneforum.org/showthread.php?t=26729)

mart_r 2021-04-23 21:56

A prime number "game of life": can floor(y*p#) always be prime?
 
1 Attachment(s)
An old pet project of mine, revamped.

If it's in any way possible I would like to turn this into a fully-fledged arXiv paper, so any suggestion on how to proceed with the work in the attachment is highly appreciated.

[I] "In this paper, the author discusses the existence of a real number y such that q = [$]\lfloor[/$]p#*y[$]\rfloor[/$] is a prime number for every p [$]\geq[/$] 2."[/I]

You may berate me for any technical or formal errors or glitches, obsolete or false statements, inappropriate verbiage or lack thereof, or for opening a new thread [SIZE=1](in my defense: this time with a fitting title, and gravedigging is considered rude just as well)[/SIZE] - but remember that [I]beraten[/I] in German means to discuss or give advice.:wink:

Batalov 2021-04-24 20:40

[QUOTE=mart_r;576673]...but remember that [I]beraten[/I] in German means to discuss or give advice.:wink:[/QUOTE]
But the ensuing discussion can also be a [I]gift[/I]. :rolleyes:

henryzz 2021-04-24 21:59

It would be nice to see a version of table 7 with primes removed if their branch has terminated in a future iteration(numbers should be monotone increasing in this case).

It is a shame that the branching rate seems to increase as the numbers get larger.

mart_r 2021-04-25 09:42

[QUOTE=Batalov;576767]But the ensuing discussion can also be a [I]gift[/I]. :rolleyes:[/QUOTE]

:lol:

[QUOTE=henryzz;576776]It would be nice to see a version of table 7 with primes removed if their branch has terminated in a future iteration(numbers should be monotone increasing in this case).

It is a shame that the branching rate seems to increase as the numbers get larger.[/QUOTE]

I've already had an idea that leads into this direction. A version of the table including the monotonely increasing number of surviving primes shouldn't pose much of a problem to me.

It would definitely be more of a discovery if there was a unique solution for a surviving branch.

xilman 2021-04-25 17:14

[QUOTE=Batalov;576767]But the ensuing discussion can also be a [I]gift[/I]. :rolleyes:[/QUOTE]The humour is going from bath to sausage.

mart_r 2021-05-14 16:30

Wuthering heights
 
1 Attachment(s)
[QUOTE=henryzz;576776]It would be nice to see a version of table 7 with primes removed if their branch has terminated in a future iteration(numbers should be monotone increasing in this case).
[/QUOTE]
Here's an updated version of Table 7, currently at level 1723. (Preliminary, as you can tell n* is backtracked from the currently calculated stage, not stage 294 as mentioned in the PDF.)
I let one laptop crunch the numbers en passant, and plan to reach level 1931 by mid June. I wouldn't go that far if it wasn't just to fill the rightmost columns.
Plus I'd also like to find a prime with ten descendants (cf. page 18 of PDF in OP).


[QUOTE=xilman;576852]The humour is going from bath to sausage.[/QUOTE]
I believe I spider...

mart_r 2021-06-23 16:05

1 Attachment(s)
Here's the updated table 7 for you, including the Pari program where I previously forgot to adjust the variable names to the text.

And here's a decuplet too: (193,057[SUP]th[/SUP] prime of s = 289) * 1,889 + {220, 238, 378, 624, 934, 1048, 1414, 1612, 1678, 1750}
where the 193,057[SUP]th[/SUP] prime of s = 289 is
[CODE]31622342567119297681076089891955816714567540280951897365387154057445488363818198016103621097928354615483039036120985961432365652251514164595044179903724253210032238290899811114046504503777054229122725692603678959245884842428958171279396512793345739562301201289205906157466250260424464347285786720763386343358970437066090084387214846787188810038323800022249321968498343734757162251150197635271251591141913929920578564323411668207833015231803312413278100502072679946962206773893320130362397698036981816468531752935920178488432680654626988222331983116303339502122373584059843024086090134096811878534903483185031614489646009414820924548284793618591561552678558457275689527829154639089241831525443509583812990724843963675707936160940952072970697432023165485601359791369860896277765474897467473349879301[/CODE]Yay! *Throws up a single confetti*[COLOR=LemonChiffon] Or is that called a confetto?[/COLOR]
Oh! Look at how the number starts off... wait... contfrac((log(a)/log(10)) = 796; 2, 41939, 2, 101, 1, 7, ... - nice!

Now at p=1931... but, you know, the year 1931 was not an especially nice one in terms of history. I'll continue to crunch the numbers down. I am unstoppable!!

[SIZE=1][COLOR=LemonChiffon]You know, it only recently occured to me that those numbers have a subtle crude sense of humour, looking at the point where the first sextuplet appears.[/COLOR][/SIZE]

mart_r 2021-06-23 20:10

[QUOTE=mart_r;581628]*Throws up a single confetti*[COLOR=LemonChiffon] Or is that called a confetto?[/COLOR]
[/QUOTE]


And that was me relying too much on German grammar, which makes it funny in a non-intentional way - and because I'm not able to edit, I just make a new post.
It should read *Throws a single confetti in the air*
See, now it's not funny anymore:davieddy:

Nick 2021-06-23 21:13

[QUOTE=mart_r;581648]
It should read *Throws a single confetti in the air*
See, now it's not funny anymore:davieddy:[/QUOTE]
That's called a confetto!

mart_r 2021-06-23 21:22

[QUOTE=Nick;581658]That's called a confetto![/QUOTE]


:davar55: I knew it! Highlight my post # 7 to check...

henryzz 2021-06-28 10:34

[QUOTE=mart_r;581628]Here's the updated table 7 for you, including the Pari program where I previously forgot to adjust the variable names to the text.

And here's a decuplet too: (193,057[SUP]th[/SUP] prime of s = 289) * 1,889 + {220, 238, 378, 624, 934, 1048, 1414, 1612, 1678, 1750}
where the 193,057[SUP]th[/SUP] prime of s = 289 is
[CODE]31622342567119297681076089891955816714567540280951897365387154057445488363818198016103621097928354615483039036120985961432365652251514164595044179903724253210032238290899811114046504503777054229122725692603678959245884842428958171279396512793345739562301201289205906157466250260424464347285786720763386343358970437066090084387214846787188810038323800022249321968498343734757162251150197635271251591141913929920578564323411668207833015231803312413278100502072679946962206773893320130362397698036981816468531752935920178488432680654626988222331983116303339502122373584059843024086090134096811878534903483185031614489646009414820924548284793618591561552678558457275689527829154639089241831525443509583812990724843963675707936160940952072970697432023165485601359791369860896277765474897467473349879301[/CODE]Yay! *Throws up a single confetti*[COLOR=LemonChiffon] Or is that called a confetto?[/COLOR]
Oh! Look at how the number starts off... wait... contfrac((log(a)/log(10)) = 796; 2, 41939, 2, 101, 1, 7, ... - nice!

Now at p=1931... but, you know, the year 1931 was not an especially nice one in terms of history. I'll continue to crunch the numbers down. I am unstoppable!!

[SIZE=1][COLOR=LemonChiffon]You know, it only recently occured to me that those numbers have a subtle crude sense of humour, looking at the point where the first sextuplet appears.[/COLOR][/SIZE][/QUOTE]

It's a shame that extending the search made so little difference lower down. From 599 to 797 the difference is only 1. I was hoping that more could be eliminated. Maybe some more could be if the easiest targets are attacked rather than everything.


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