20210304, 15:08  #1 
"David Kirkby"
Jan 2021
Althorne, Essex, UK
2^{4}·7 Posts 
Marked "no factors below 2^74" after two LL tests.
The exponent 60074291
https://www.mersenne.org/report_expo...0074291&full=1 has a status of "No factors below 2^74". I'm puzzled why this is so, given Koekie performed a LL test in 2016 and get a residual of 0B368C0C78A5DBFD, then I performed the L:L test a few weeks ago and got the same residual. Does that not prove beyond all reasonable doubt that 2^60074291 1 is composite? I'm not sure how to interpret the webpage. I can see the statement it has no factors below 2^74 is, but it's not clear that the number is composite, even though we don't know a factor. Last fiddled with by drkirkby on 20210304 at 15:09 
20210304, 15:16  #2 
"Oliver"
Sep 2017
Porta Westfalica, DE
1D5_{16} Posts 
That message only means what is displayed, that we did not a factor (yet) and that we are somewhat sure that we have to look for factors above 2^{74}. The compositeness is indeed beyond reasonable doubt at this point, but not mentioned with this exact wording. "Verified" in the row "LL" or "PRP" in the column "status" (not the outer one, there are two named the same, unfortunately) is what should be read as "verified composite". If it was prime, it would look like e.g. M82589933.
The information about how far we have searched for factors is still useful for those who like to find factors for already known composite Mersenne numbers. 
20210305, 16:38  #3 
"Matthew Anderson"
Dec 2010
Oregon, USA
1314_{8} Posts 
Welcome to mersenneforum !!!

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