Missed Primes
 

R. De Troia found this:

[url=http://primes.utm.edu/primes/page.php?id=85865]31*2^406105-1[/url]

although this k was tested to n=1.3M !?!?

I marked the range with a questionmark and with a '(...)' for the prime n's.

k=31 was reported as tested to 500k by Steven (L1), and I think another Steven (L330) started from there. I'm not aware of L1 missing any primes, or reporting false ones, but at the time when he did his tests there were some buggy versions of LLR floating around.

I did start this k=31 from 500k & up.

-Steven

L637 reported one more k=31 prime:

31*2^421129-1

I wrote to Steven, and asked him whether he has any idea how he missed them.

I remember Jean said that the bug in early LLR versions didn't affect small Ks, but he never said what does "small" exactly mean. Maybe k=31 was not small enough?

NPLB has double-checked all k<=25 for n=100K-260K. The next k<300 range to double-check in that drive is k=27-31 for n=100K-260K. I'll run that range after our 1st drive is done in ~2 weeks. At least we'll then know that k=31 is good to n=260K since n<100K was previously double-checked a long time ago.

Personally, I don't think the first Steven (L1) tested it up to n=500K. The chances of even "somewhat" buggy software missing 2 primes in a small range like that are very remote. I suspect he mixed up his k's or ranges when he reported them.


Gary

Too bad the new Steven (my student) didn't start at 400k.. He would have been excited to find two primes so quickly!
-Curtis

Yet another one found by Steven, who is double-checking k=29:
29*2^347896-1

I'm afraid the problem was one of first, early verions of LLR, which was known to have bugs. The relevant link is [URL="http://www.mersenneforum.org/showthread.php?t=2985"]here[/URL]. That's LLR time-stamped March 22, 2004. It was not corrected before September 2004.

another one
 

I also found 27*2^282700-1 last month. I am currently checkinh, 5, 7, 9, 11, 13, 15, 19, 21 ,23, 25, 27, 29 from 260k to 500k.


Steven Harvey

want to help? with recheck?
 

If anyone wants to assist, I'd be happy to send you a presieved range for any of these k, 5,7,9,11, 13, 15, 19, 21, 23, 25, 27, 29. I am currently up to at least 280k on all, & higher on 27 and 29.

Steven Harvey

k=25 tested from n=400000 using LLR version 3.62 (AFAIR). If someone really wants to perform doublecheck on this one, then I can provide result file for comparison :smile:

25 result file
 

I would like the 25 from 400k result file for comparison purposes.
Please send it to me or post it here, zipped preferably. When did you do the check?? Thanks!