20120128, 22:34  #1 
"Daniel Jackson"
May 2011
14285714285714285714
648_{10} Posts 
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?

20120128, 23:20  #2 
Mar 2006
Germany
43×67 Posts 
So far there're no primes listed at the Top5000 (Riesel or Sierptype).
I've also none listed on my pages. With a Riesel Nash weight of 750 it's a low weight kvalue, so not that much primes to find but less work to sieve. Here're are some other notes for that kvalue:  Prime curious  good to know  or this one  many such telephone numbers 
20120129, 00:14  #3 
Aug 2010
Kansas
547 Posts 
FWIW
Just for fun, I sieved 050k k values for n=8675309 up to 71B or so, 2222 remaining candidates. I'll start the fixedk sieve in a minute :)

20120129, 00:26  #4 
Mar 2006
Germany
101101000001_{2} Posts 
As mentioned in another thread:
8675309*2^n1 is prime for n=4, 40, 84, 212, 720, 1512, 9344, 44160 (tested to n=50k) 
20120129, 00:29  #5 
Aug 2010
Kansas
547 Posts 
k=8675309, n=50k250k is down to 4780 candidates after 1B sieve.

20120129, 01:44  #6 
Nov 2003
2×1,811 Posts 
This particular k can have primes of form k*2^n1 only for exponents n divisible by 4 so the answer to your question is no. However p=29983*2^8379431 is prime and both k and n are primes, and there are many more such examples for larger k's.

20120129, 02:13  #7 
Nov 2003
2·1,811 Posts 
Here is the largest k*2^n1 prime on Top5000 where both k and n are primes and k>10^6
3039469*2^9286431 
20120129, 09:15  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,391 Posts 
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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