20210423, 21:56  #1 
Dec 2008
you know...around...
677_{10} 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 fullyfledged 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. 
20210424, 20:40  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×3×797 Posts 

20210424, 21:59  #3 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5×7×13^{2} 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. 
20210425, 09:42  #4  
Dec 2008
you know...around...
677 Posts 
Quote:
It would definitely be more of a discovery if there was a unique solution for a surviving branch. 

20210425, 17:14  #5 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10101011000110_{2} Posts 

20210514, 16:30  #6  
Dec 2008
you know...around...
677 Posts 
Wuthering heights
Quote:
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). I believe I spider... 

20210623, 16:05  #7 
Dec 2008
you know...around...
1245_{8} 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: (193,057^{th} prime of s = 289) * 1,889 + {220, 238, 378, 624, 934, 1048, 1414, 1612, 1678, 1750} where the 193,057^{th} prime of s = 289 is Code:
31622342567119297681076089891955816714567540280951897365387154057445488363818198016103621097928354615483039036120985961432365652251514164595044179903724253210032238290899811114046504503777054229122725692603678959245884842428958171279396512793345739562301201289205906157466250260424464347285786720763386343358970437066090084387214846787188810038323800022249321968498343734757162251150197635271251591141913929920578564323411668207833015231803312413278100502072679946962206773893320130362397698036981816468531752935920178488432680654626988222331983116303339502122373584059843024086090134096811878534903483185031614489646009414820924548284793618591561552678558457275689527829154639089241831525443509583812990724843963675707936160940952072970697432023165485601359791369860896277765474897467473349879301 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. 
20210623, 20:10  #8 
Dec 2008
you know...around...
1245_{8} Posts 
And that was me relying too much on German grammar, which makes it funny in a nonintentional 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 20210623 at 20:14 
20210623, 21:13  #9 
Dec 2012
The Netherlands
2^{4}·109 Posts 

20210623, 21:22  #10 
Dec 2008
you know...around...
677 Posts 

20210628, 10:34  #11  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5·7·13^{2} Posts 
Quote:


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