Closest you've come to finding a new Mersenne Prime?

MooMoo2 · 2018-12-21, 17:54

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 first-time test that was completed before the prime it was closest to was announced.

cuBerBruce · 2018-12-21, 19:08

My closest was exponent 77232521, only 396 under the exponent for the (provisional) M50. It was only 24 primes away from that exponent.

kriesel · 2018-12-21, 20:17

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.

Quote:

Originally Posted by cuBerBruce

It was only 24 primes away from that exponent.

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.

GP2 · 2018-12-21, 20:45

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.

kriesel · 2018-12-21, 23:59

Quote:

Originally Posted by GP2

We'll never know, because it all depends how you define "close".

The first post in the thread seems to clearly mean exponent value proximity. Least delta p from a composite test to a discovered prime, no later in time than the discovered Mersenne prime it's near.

cuBerBruce · 2018-12-22, 00:52

Quote:

Originally Posted by kriesel

The first post in the thread seems to clearly mean exponent value proximity. Least delta p from a composite test to a discovered prime, no later in time than the discovered Mersenne prime it's near.

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.

The Carnivore · 2019-01-06, 18:37

The closest would have to be George Woltman:
https://primes.utm.edu/notes/1257787.html

Quote:

On 3 September 1996, Cray Research announced that once again Slowinski and Gage have set a new record by finding the prime 2^1257787-1 which has 378,632 digits.
...
The proof of this 378,632 digit number's primality (using the traditional Lucas-Lehmer test) took about 6 hours on one CPU of a CRAY T94 super computer. Richard Crandall and others independently verified the primality. The first and the most interesting of these was George Woltman who was 90% of the way through that very number when asked to check the result on April 15th. According to the San Jose Mercury News article he said "It hurt for a few days, but I got over it." Woltman's program is available over the Internet and will check this new prime in about 60 hours on a 90MHz Pentium.

GP2 · 2019-01-06, 19:05

Quote:

Originally Posted by The Carnivore

Quote:

On 3 September 1996, Cray Research announced that once again Slowinski and Gage have set a new record by finding the prime 2^1257787-1 which has 378,632 digits.
...
The proof of this 378,632 digit number's primality (using the traditional Lucas-Lehmer test) took about 6 hours on one CPU of a CRAY T94 super computer.

Slowinski and Gage considered using an Android phone app instead of a Cray, but it would have been too slow...

ATH · 2019-01-06, 19:28

Quote:

Originally Posted by The Carnivore

The closest would have to be George Woltman:

https://www.mersenne.org/newsletters/?id=6

Quote:

On April 15, David asked me to verify his new find. Ironicly, at the
time I received his email, my own Pentium-90 was 95% of the way through
testing that exponent. That hurt for a few days! However, I also saw a
lot of positives. Despite a two-year head start, David found the new
prime only a few days before we did. Furthermore, our effort was just
getting under way, we now have more than 4 times as many searchers as
we did then. I firmly believe that the 35th Mersenne prime will be
found by a member of our group! I have but one regret: After picking
the lucky 1257 range, I wish I had run it on my Pentium Pro 200 instead
of the Pentium-90!

kriesel · 2019-01-06, 20:07

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.

Uncwilly · 2019-01-07, 01:09

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.

2018-12-21, 17:54	#1
MooMoo2 Aug 2010 1133₈ 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 first-time test that was completed before the prime it was closest to was announced.

2018-12-21, 20:45	#4
GP2 Sep 2003 3²·7·41 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 2018-12-21 at 20:46

2019-01-06, 20:07	#10
kriesel "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 3·5·17·19 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 2019-01-06 at 20:09

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2018-12-21, 19:08	#2
cuBerBruce 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.

2019-01-07, 01:09	#11
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×3²×7×73 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.