mersenneforum.org 2*b^n-1, b<=2048
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 2019-07-10, 13:44 #1 LaurV Romulan Interpreter     Jun 2011 Thailand 100010100011012 Posts 2*b^n-1, b<=2048 I lost that thread which would make Sweety happy... But here we are. 2*2018^145464-1 is prime! (480748 decimal digits, P = 4) Time : 10107.913 sec. Does it worth reporting to top5k? Any idea what's the lowest digits tail? (hey, 14-54-64 is this random? hehe) There are 19 "bases" left below 2048 for which a prime is unknown. All are tested to over n=110k, and few of them reached n=200k where we stopped, waiting for all bases to reach n=200k. Last fiddled with by LaurV on 2019-07-10 at 13:49 Reason: extra line spacing is killing us... also s/16/19/ bases left (typo)
2019-07-10, 13:47   #2
paulunderwood

Sep 2002
Database er0rr

11×313 Posts

Quote:
 Originally Posted by LaurV 2*2018^145464-1 is prime! (480748 decimal digits, P = 4) Time : 10107.913 sec. Does it worth reporting to top5k? Any idea what's the lowest digits tail? (hey, 14-54-64 is this random? hehe)
According to https://primes.utm.edu/primes/status.php

Quote:
 We at the Prime Pages attempt to keep a list of the 5000 largest known primes plus a few each of certain selected archivable forms. To make the top 5000 today a prime must have 425901 digits or meet the size requirements for it's archivable form. (Query time: 0.001631 seconds.)
So yes! Congrats on a top5000

To get the tail use print(2*2018^145464-1) in pari/gp

Last fiddled with by paulunderwood on 2019-07-10 at 13:54

2019-07-10, 14:12   #3
LaurV
Romulan Interpreter

Jun 2011
Thailand

884510 Posts

Quote:
 The following warnings have been noted: At the rate at which primes have been added to this list in the past, the 480748 digit prime "2*2018^145464-1" may only be on the list for about 33 weeks.
hehe...
Thanks Paul

Edit: by "tail" I was meaning the tail of the list (the lowest digits count, or as it is called, size requirement), not the decimal representation of the prime, but thanks anyhow for that too

Last fiddled with by LaurV on 2019-07-10 at 14:15

2019-07-10, 14:21   #4
paulunderwood

Sep 2002
Database er0rr

11·313 Posts

Quote:
 Originally Posted by LaurV hehe... Thanks Paul Edit: by "tail" I was meaning the tail of the list (the lowest digits count, or as it is called, size requirement), not the decimal representation of the prime, but thanks anyhow for that too

 2019-07-10, 18:55 #5 sweety439     Nov 2016 2×11×107 Posts LaurV edit: rubbish deleted, attachments removed You won't pollute my blog with that. Sorry. Last fiddled with by LaurV on 2019-07-11 at 12:07
 2019-07-10, 18:59 #6 sweety439     Nov 2016 93216 Posts Do you have the file for the smallest k>=1 such that 2*n^k-1 is prime for n<=2048? Last fiddled with by LaurV on 2019-07-11 at 12:08 Reason: quote of full post removed
2019-07-10, 19:58   #7
kar_bon

Mar 2006
Germany

54428 Posts

Quote:
 Originally Posted by LaurV I lost that thread which [...]
See here for some data and the link to the forum thread.

2019-07-10, 20:28   #8
sweety439

Nov 2016

2·11·107 Posts

Quote:
 Originally Posted by kar_bon See here for some data and the link to the forum thread.
But this data is only for bases <= 1024

 2019-07-10, 21:18 #9 kar_bon     Mar 2006 Germany 2×3×52×19 Posts So where's the problem? The data can be extended/inserted for k=2 for n>1030.
2019-07-11, 12:15   #10
LaurV
Romulan Interpreter

Jun 2011
Thailand

5·29·61 Posts

Quote:
 Originally Posted by sweety439 Do you have the file for the smallest k>=1 such that 2*n^k-1 is prime for n<=2048?
Yes. It was posted in the past. There is no new stuff in it beside the only one prime found between n=100k and 200k, which I posted here.
I am still actively working this "pet project" but the machines used are slow.

More to come soon, give me few hours to arrive home.

 2019-08-29, 12:58 #11 LaurV Romulan Interpreter     Jun 2011 Thailand 100010100011012 Posts 2*1595^175532-1 is prime! (562188 decimal digits) 18 to go Reported to UTM, waiting verification.