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...

22·163 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, 28 views)

2021-04-24, 20:40   #2
Batalov

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

2·53·89 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 Cambridge (GMT/BST) 2×5×587 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...

22·163 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!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

1068310 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...

10100011002 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, 6 views)

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