mersenneforum.org k=8675309, Any primes?
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 2012-01-28, 22:34 #1 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 22·3·59 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?
 2012-01-28, 23:20 #2 kar_bon     Mar 2006 Germany 2·1,481 Posts 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
2012-01-29, 00:14   #3
c10ck3r

Aug 2010
Kansas

547 Posts
FWIW

Quote:
 Originally Posted by Stargate38 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 :)

 2012-01-29, 00:26 #4 kar_bon     Mar 2006 Germany B9216 Posts 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)
 2012-01-29, 00:29 #5 c10ck3r     Aug 2010 Kansas 22316 Posts k=8675309, n=50k-250k is down to 4780 candidates after 1B sieve.
2012-01-29, 01:44   #6
Kosmaj

Nov 2003

2·1,811 Posts

Quote:
 Originally Posted by Stargate38 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.

 2012-01-29, 02:13 #7 Kosmaj     Nov 2003 2×1,811 Posts 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
 2012-01-29, 09:15 #8 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23×32×137 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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