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Old 2019-07-10, 13:44   #1
LaurV
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Default 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)
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Old 2019-07-10, 13:47   #2
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Quote:
Originally Posted by LaurV View Post
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
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Old 2019-07-10, 14:12   #3
LaurV
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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
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Old 2019-07-10, 14:21   #4
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Quote:
Originally Posted by LaurV View Post
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
https://primes.utm.edu/primes/download.php will get you to the complete top5000 list.
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Old 2019-07-10, 18:55   #5
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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
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Old 2019-07-10, 18:59   #6
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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
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Old 2019-07-10, 19:58   #7
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Quote:
Originally Posted by LaurV View Post
I lost that thread which [...]
See here for some data and the link to the forum thread.
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Old 2019-07-10, 20:28   #8
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Originally Posted by kar_bon View Post
See here for some data and the link to the forum thread.
But this data is only for bases <= 1024
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Old 2019-07-10, 21:18   #9
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So where's the problem? The data can be extended/inserted for k=2 for n>1030.
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Old 2019-07-11, 12:15   #10
LaurV
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Quote:
Originally Posted by sweety439 View Post
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.
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Old 2019-08-29, 12:58   #11
LaurV
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2*1595^175532-1 is prime! (562188 decimal digits)


18 to go


Reported to UTM, waiting verification.


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