mersenneforum.org A prime number "game of life": can floor(y*p#) always be prime?
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2021-04-23, 21:56   #1
mart_r

Dec 2008
you know...around...

22·11·17 Posts
A prime number "game of life": can floor(y*p#) always be prime?

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.

"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."

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 (in my defense: this time with a fitting title, and gravedigging is considered rude just as well) - but remember that beraten in German means to discuss or give advice.
Attached Files
 Project_p#Y.pdf (314.7 KB, 136 views)

2021-04-24, 20:40   #2
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23·1,229 Posts

Quote:
 Originally Posted by mart_r ...but remember that beraten in German means to discuss or give advice.
But the ensuing discussion can also be a gift.

 2021-04-24, 21:59 #3 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 32×5×7×19 Posts 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.
2021-04-25, 09:42   #4
mart_r

Dec 2008
you know...around...

2EC16 Posts

Quote:
 Originally Posted by Batalov But the ensuing discussion can also be a gift.

Quote:
 Originally Posted by henryzz 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.
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.

2021-04-25, 17:14   #5
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

260708 Posts

Quote:
 Originally Posted by Batalov But the ensuing discussion can also be a gift.
The humour is going from bath to sausage.

2021-05-14, 16:30   #6
mart_r

Dec 2008
you know...around...

2EC16 Posts
Wuthering heights

Quote:
 Originally Posted by henryzz 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).
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:
 Originally Posted by xilman The humour is going from bath to sausage.
I believe I spider...
Attached Files
 Table_7.pdf (55.5 KB, 92 views)

2021-06-23, 16:05   #7
mart_r

Dec 2008
you know...around...

22·11·17 Posts

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: (193,057th prime of s = 289) * 1,889 + {220, 238, 378, 624, 934, 1048, 1414, 1612, 1678, 1750}
where the 193,057th prime of s = 289 is
Code:
31622342567119297681076089891955816714567540280951897365387154057445488363818198016103621097928354615483039036120985961432365652251514164595044179903724253210032238290899811114046504503777054229122725692603678959245884842428958171279396512793345739562301201289205906157466250260424464347285786720763386343358970437066090084387214846787188810038323800022249321968498343734757162251150197635271251591141913929920578564323411668207833015231803312413278100502072679946962206773893320130362397698036981816468531752935920178488432680654626988222331983116303339502122373584059843024086090134096811878534903483185031614489646009414820924548284793618591561552678558457275689527829154639089241831525443509583812990724843963675707936160940952072970697432023165485601359791369860896277765474897467473349879301
Yay! *Throws up a single confetti* Or is that called a confetto?
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!!

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.
Attached Files
 Table_7.pdf (69.5 KB, 77 views)

2021-06-23, 20:10   #8
mart_r

Dec 2008
you know...around...

22·11·17 Posts

Quote:
 Originally Posted by mart_r *Throws up a single confetti* Or is that called a confetto?

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

Last fiddled with by mart_r on 2021-06-23 at 20:14

2021-06-23, 21:13   #9
Nick

Dec 2012
The Netherlands

6DF16 Posts

Quote:
 Originally Posted by mart_r It should read *Throws a single confetti in the air* See, now it's not funny anymore
That's called a confetto!

2021-06-23, 21:22   #10
mart_r

Dec 2008
you know...around...

22·11·17 Posts

Quote:
 Originally Posted by Nick That's called a confetto!

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

2021-06-28, 10:34   #11
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

32×5×7×19 Posts

Quote:
 Originally Posted by mart_r 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: (193,057th prime of s = 289) * 1,889 + {220, 238, 378, 624, 934, 1048, 1414, 1612, 1678, 1750} where the 193,057th prime of s = 289 is Code: 31622342567119297681076089891955816714567540280951897365387154057445488363818198016103621097928354615483039036120985961432365652251514164595044179903724253210032238290899811114046504503777054229122725692603678959245884842428958171279396512793345739562301201289205906157466250260424464347285786720763386343358970437066090084387214846787188810038323800022249321968498343734757162251150197635271251591141913929920578564323411668207833015231803312413278100502072679946962206773893320130362397698036981816468531752935920178488432680654626988222331983116303339502122373584059843024086090134096811878534903483185031614489646009414820924548284793618591561552678558457275689527829154639089241831525443509583812990724843963675707936160940952072970697432023165485601359791369860896277765474897467473349879301 Yay! *Throws up a single confetti* Or is that called a confetto? 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!! 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.
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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