20080626, 18:44  #1 
5^{3}×59 Posts 
Wrong entries in database?
I just looked at the status of a few small exponents and I discovered sth. strange: Some (small) exponents seem to have wrong LLTest marked as "Verified LL":
Here are three examples: M10061 No factors below 2^59 P1 B1=2147483647 Verified LL 3188 by "Unknown" Verified LL 56EB9BB91825B188 by "George Woltman" Verified LL 56EB9BB91825B188 by "Brian J. Beesley" M10399 No factors below 2^58 P1 B1=4290000000 Verified LL 151E by "Unknown" Verified LL 7D445D0CFC69951E by "George Woltman" Verified LL 7D445D0CFC69951E by "Brian J. Beesley" M10667 No factors below 2^58 P1 B1=1000000000 Verified LL 5B7B by "Unknown" Verified LL AD23A344EA29DB7B by "George Woltman" Verified LL AD23A344EA29DB7B by "Brian J. Beesley" History 430 curves, B1=1000000, B2=100000000 by "ANONYMOUS" on 20070927 Some 16bit LLResidues submitted by "Unknown" seem to be wrong (M10061: "...151E" instead of th correct "...951E"). This is  as far as I'm understanding this  an error and should be corrected. I haven't the time to check more exponents, so I wrote it in the forum... PS: Here's the direct link I used: http://v5www.mersenne.org/report_exp...&B1=Get+status 
20080626, 19:13  #2 
Mar 2008
2^{5} Posts 
Probably because the 16 bit residues are actually 15 bits (perhaps the top bit is a flag for something).
Ex (from your residues): 3 hex = 0011 binary B hex = 1011 binary 1 hex = 0001 binary 9 hex = 1001 binary 5 hex =0101 binary D hex =1101 binary Just a guess. 
20080628, 01:14  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
I was just going to say the same: The fourhexadecimaldigit residues represent only 15bit values.
Thank you anyway, "Unregistered", for your concern about this project and for taking the time and initiative to start this thread to ask your question !!! Your next question might lead to something that does need correction. In fact, this one does point out a needed change, too: GIMPS documentation may not yet have an explanation, or as prominent a one as is needed, of the apparent discrepancy you noticed. Thank you. Last fiddled with by cheesehead on 20080628 at 01:59 
20080628, 01:27  #4 
P90 years forever!
Aug 2002
Yeehaw, FL
3^{2}×823 Posts 
The 2 explanations are correct. I'm loathe to eliminate the small residues as these are in many cases, to the best of my knowledge, the very first LL test on the number.

20080628, 01:50  #5 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
... and the small residues shouldn't be eliminated. They are as genuine as the large ones.
   George, I need to put a definite date on my calendar (before the end of summer, say) for compiling my documentation suggestions and presenting proposed updated versions of various pages and text files to you. Please ask me about this if you don't see it by October. Last fiddled with by cheesehead on 20080628 at 02:02 
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