20210420, 21:52  #243  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22367_{8} Posts 
DRUG is PRP 2nd top now :wink:
Quote:


20210420, 22:08  #244  
Sep 2002
Database er0rr
E70_{16} Posts 
Quote:


20210527, 11:14  #245 
Mar 2006
Germany
101101010010_{2} Posts 
Riesel problem
After years of work from RieselSieve and further testing/sieving/double checking by PrimeGrid there are currently 44 kvalues left for which no prime k*2^n1 was found yet.
After three primes found by Ryan Propper this year for the Riesel problem and a post from him at the PG forum, which says he's "doing some solo hunting" work for 12M<=n<=15M (but not explicitly given which kvalues), PrimeGrid seems stopped the search for those 3 found kvalues according to their status page showing they stopped checking at n~11.5M. So this will leave a range of uncertainty if there eventually exists a smaller prime than those found ones. Open questions:  Will PG check the missing ranges?  Is Ryan Propper testing further ranges/kvalues? If so, which ones? Before this is cleared, the Riesel problem still stay at 47 open kvalues left to prove the problem and I think neither Wilfrid Keller nor any serious prime hunter will rest until this inconsistency is resolved. To all: please comunicate your search and make them available to avoid duplicate work. 
20210527, 18:07  #246  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,463 Posts 
Quote:
But a simple question arises  can these three k values be Riesel numbers? They cannot. Then why is it relevant how big the witness primes are? Does this conjecture need two witness primes  i.e. these known ones, and the slightly smaller ones? It does not. Am I missing something? 

20210527, 23:38  #247 
Mar 2019
2·5·17 Posts 
These are both your opinions, and the former is clearly false.

20210529, 01:25  #248 
"Alexander"
Nov 2008
The Alamo City
653 Posts 
The Riesel problem, by definition, is proving whether 509,203 is the smallest Riesel number. These 3 k's, with prime n's now known, are no longer relevant for that problem. They cannot be the smallest Riesel number. While it would be useful to know the smallest primes for each k, this is not directly related to the Riesel problem as defined. There are 44 k's left in the Riesel problem, corresponding to the 44 Riesel k's less than 509,203 with no primes known.

20210529, 08:12  #249 
Mar 2006
Germany
2×3^{2}×7×23 Posts 
I've updated the Wiki page with those notPGfoundprimes, unreserved them, so no longer listed in their project page, but still left a note for those 3 kvalues.
Sure the Riesel problem is to find any nvalue of any of the remianing kvalues to prove the conjecture. But from beginning the project every real primesearcher like Keller or Gallot were anxious to know the lowest nvalue. This also prevents to fill in the missing value for k=2293 in this OEIS sequence, because this lists only the lowest n. Because I could not determine the date when PG stopped the search for those values, I took the 20210501 and the maxn value of the search from their status page. 
20210529, 16:51  #250 
Mar 2019
2·5·17 Posts 
It does not help your arguments to claim that you are a "real" primesearcher (sp) and others are not, whatever that means.

20210530, 11:07  #251 
Mar 2006
Germany
2·3^{2}·7·23 Posts 
I've not claimed me a real primesearcher, but thank you for the title.
I'm collecting data in prime numbers for k*2^n1 (mostly and others, too) for 14 years now (my first page for RPS was in 2007), because there was no data collection in an oversesable form: many small personal projects, some others only testing some ranges, and all data spread around the net. You even don't know how much work I've done over the years and how disappointing it is to see only a prime and no further information like tested ranges. So even if somebody is logged in here, why no further information should be given? In the primesearch community nothing is more annoying to test open ranges to fill some missing data. That's my real concern: to document the whole data to avoid duplicate and disappointing work for others. 
20210530, 18:17  #252 
Feb 2019
89 Posts 
Just wanted to let you know that your efforts are greatly appreciated, kar_bon!

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