20181221, 17:54  #1 
Aug 2010
2·311 Posts 
Closest you've come to finding a new Mersenne Prime?
For those of you who were unsuccessful (which is most of us!), what exponent have you tested that was the nearest to a Mersenne prime's exponent? Mine was 82,612,457, which was not too far off M51 (82,589,933).
Note: In order for it to count, it needs to be a firsttime test that was completed before the prime it was closest to was announced. 
20181221, 19:08  #2 
Aug 2012
Mass., USA
2·3·53 Posts 
My closest was exponent 77232521, only 396 under the exponent for the (provisional) M50. It was only 24 primes away from that exponent.

20181221, 20:17  #3 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
140D_{16} Posts 
I've run most of them, more than once, as in software development & QA testing. But discovering one, running one correctly to completion before anyone else? Closest assignment I've run was 77231809, 1108 lower than M50*, just 14.35ppm too low. I think it was issued 9 days earlier than the "winning ticket". Felt like a near miss at the time.
There are enough prime exponents in +1108 interval that probably a lot of people got closer. Have you considered reserving a contiguous block of 25 at a time? A miss is as good as a mile. The assignment 77231809 happened to land on the slowest and least reliable box I had running at the time. A wrong LL/Jacobi would have been very likely. It was run on PRP/GC and hit a point it could not make further progress. It was moved to another faster reliable system and run to completion, and repeated from scratch, on prime95v29.5b1, and matched. Prime95 PRP/GC passed that acid test imposed by unreliable hardware. Last fiddled with by kriesel on 20181221 at 20:24 
20181221, 20:45  #4 
Sep 2003
2×5×7×37 Posts 
We'll never know, because it all depends how you define "close".
A Mersenne semiprime is "close" to being a Mersenne prime. But we have no way to count the number of factors for the overwhelming majority of composite Mersenne numbers, and no way to discover the overwhelming majority of Mersenne semiprimes, since the smaller factor will most often be larger than a few hundred bits. Last fiddled with by GP2 on 20181221 at 20:46 
20181221, 23:59  #5 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3×29×59 Posts 

20181222, 00:52  #6 
Aug 2012
Mass., USA
476_{8} Posts 
Well, in my case, my composite result was reported to the server before the nearby Mersenne prime was officially announced. I believe that makes it compliant with the OP's rules.

20190106, 18:37  #7  
Jun 2010
251 Posts 
The closest would have to be George Woltman:
https://primes.utm.edu/notes/1257787.html Quote:


20190106, 19:05  #8  
Sep 2003
2·5·7·37 Posts 
Quote:


20190106, 19:28  #9  
Einyen
Dec 2003
Denmark
2·1,567 Posts 
https://www.mersenne.org/newsletters/?id=6
Quote:


20190106, 20:07  #10 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3×29×59 Posts 
Another way to look at it is the nearest composite exponent primality test completed before a neighboring prime's test is completed. (nearest miss in exponent value space) The record for that is 4 on exponent value. See the attachment at https://www.mersenneforum.org/showpo...87&postcount=2
But yeah, that had to hurt when George got the call. I hope he took a photo of the display with the run status and date and time visible, for his journal. Last fiddled with by kriesel on 20190106 at 20:09 
20190107, 01:09  #11 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2·3·1,597 Posts 
I relayed the jist of this story to someone today at church. They are building a new machine and I told them that they should check it with Prime95.

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