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Old 2012-01-28, 22:34   #1
Stargate38
 
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Default k=8675309, Any primes?

How many primes have been found for k=8675309? I love taking notes of large primes with k prime as well. Do any of them have a prime n value?
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Old 2012-01-28, 23:20   #2
kar_bon
 
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So far there're no primes listed at the Top5000 (Riesel or Sierp-type).
I've also none listed on my pages.

With a Riesel Nash weight of 750 it's a low weight k-value, so not that much primes to find but less work to sieve.

Here're are some other notes for that k-value:
- Prime curious
- good to know
- or this one
- many such telephone numbers
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Old 2012-01-29, 00:14   #3
c10ck3r
 
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Default FWIW

Quote:
Originally Posted by Stargate38 View Post
How many primes have been found for k=8675309? I love taking notes of large primes with k prime as well. Do any of them have a prime n value?
Just for fun, I sieved 0-50k k values for n=8675309 up to 71B or so, 2222 remaining candidates. I'll start the fixed-k sieve in a minute :)
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Old 2012-01-29, 00:26   #4
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As mentioned in another thread:

8675309*2^n-1 is prime for n=4, 40, 84, 212, 720, 1512, 9344, 44160 (tested to n=50k)
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Old 2012-01-29, 00:29   #5
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k=8675309, n=50k-250k is down to 4780 candidates after 1B sieve.
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Old 2012-01-29, 01:44   #6
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Quote:
Originally Posted by Stargate38 View Post
How many primes have been found for k=8675309? I love taking notes of large primes with k prime as well. Do any of them have a prime n value?
This particular k can have primes of form k*2^n-1 only for exponents n divisible by 4 so the answer to your question is no. However p=29983*2^837943-1 is prime and both k and n are primes, and there are many more such examples for larger k's.
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Old 2012-01-29, 02:13   #7
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Here is the largest k*2^n-1 prime on Top-5000 where both k and n are primes and k>10^6

3039469*2^928643-1
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Old 2012-01-29, 09:15   #8
Batalov
 
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Another small Sierp. prime with k and n prime:
43112609*2^64081+1
This k looks familiar from some other thread...
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