20060827, 01:03  #1 
May 2003
7·13·17 Posts 
Sieved?
I'm wondering if Cunningham numbers on the 3 and 3+ tables have been completely factored for small factors up to a specific size. In particular, I'm wondering if something like the following is true:
All numbers of the form 3^n1 for 1000<n<100,000 must have a factor larger than 10^40. 
20060827, 02:55  #2  
"Phil"
Sep 2002
Tracktown, U.S.A.
2×13×43 Posts 
Quote:
I suspect that many numbers in this range may have not been tested beyond 25 digits, judging from my experience with the 2 and 2+ tables. 

20060827, 03:00  #3 
May 2003
60B_{16} Posts 
Actually 25 digits would still be interesting (if it is true that they've all been tested up to this level).

20060827, 09:40  #4  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24415_{8} Posts 
Quote:
I certainly didn't win the competition. I forget the precise details but my guess was something like 2 remaining and 3 were duly found. The consensus is that it is now very unlikely that there are any prime factors with fewer than 40 digits still to be discovered. None have been found this year. The smallest reported is P43 and there are 30 in my table for 2006 which arel under P50. There may be one or two mpre P4x to be added when I bring my table up to date. Paul 

20060827, 09:46  #5  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3×31×113 Posts 
Quote:
I do not know of any tabulations of factorizations of the numbers in question. It would be easy enough to create such tables if they don't exist. If any are in existence, I doubt they would be complete much beyond p20 or so. Paul 

20060828, 13:45  #6 
May 2003
7×13×17 Posts 
xilman,
If they are not techinically Cunningham numbers (yet), they are in the same spirit. But, I would even be happy to know they have been checked up to 20 digits. The reason I ask is that, with the search for Mersenne primes, we do a lot of sieving for small factors. I was wondering if the same is done for the 3 tables (up to large exponents). 
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