Lucky 13 (M51 related)

[Prime95]

Originally Posted by kriesel

Looking back through mersenne.org, I see some exponents determined prime also have (anonymous) incorrect composite LL indications; https://www.mersenne.org/report_expo...exp_hi=&full=1
https://www.mersenne.org/report_expo...exp_hi=&full=1
https://www.mersenne.org/report_expo...exp_hi=&full=1
https://www.mersenne.org/report_expo...exp_hi=&full=1

We ought to clean that junk out of the database. The server will reject duplicate prime results for known Mersenne primes. However, it seems the server is not rejecting composite results for known Mersenne primes.

[kriesel]

Originally Posted by Prime95

We ought to clean that junk out of the database. The server will reject duplicate prime results for known Mersenne primes. However, it seems the server is not rejecting composite results for known Mersenne primes.

By all means clean out those erroneous composite results on known Mersenne primes. The TF and P-1 clutter on already-confirmed primes is a separate decision or two, which I feel should be removed, and prevented from reoccurring.

I'd like to see the false P-1 assignment expiration entries on unknown-status exponents gone too. (see https://www.mersenneforum.org/showthread.php?t=23817 for some known cases and a theory about a cause.)

[Madpoo]

Originally Posted by Uncwilly

I've noticed some interesting names with some interesting exponent assignments that will be "home for the holidays" as it were.

MD5 hash guess of one that looks tasty (includes exponent assignee MM/DD expected completion date)
227a10ba5bbe1b4b033c2983ee417ee9

It does fit the 2 requirements posted by George and Alex. There also appears to be some funny business in the history on the assignment page.

I'm trying to check your result but I can't quite figure out what your string looks like before hashing...

Do you mean it looks like "12345678Madpoo1210" or do you have spaces and the slash between MM/DD in there, or... ?

EDIT: wait, I tried adding spaces and the slash - I see the exponent you mean, and my hint that it's not a previous discoverer would rule that one out.

[kriesel]

Originally Posted by Madpoo

Smarter folks than I can weigh in, like George did in mentioning that PRP is the future...

Here's my understanding: PRP is probabilistic and LL is deterministic. So although a PRP can say "M###" is probably prime, an LL test can say "M###" is prime.

PRP tests have the benefit of the Gerbicz error checking code that may make double-checking the tests unnecessary.

As to just how probable the PRP tests are, I understand that when PRP says it's probably prime, that probability is VERY high. And when I say the PRP error checking makes double-checks obsolete, I think that's generally true although I foresee cases where spot-checks make sense, but overall that's where I think it's headed. If I'm wrong in my assumptions, someone will correct me I'm sure.

When it comes to finding a new Mersenne Prime, I guess the question about whether a probable finding is good enough to be accepted, or would the LL test be required before it's confirmed. Maybe that's similar to how we already verify a prime using different software - it's a way of ensuring there aren't any code issues or other obscure things.

Very "on the money". And if there's a PRP discovery, I think it likely we confirm the PRP residue with a PRP run on different software & hardware, but the real mathematically acceptable proof will still be LL runs on different software and different hardware. In this case, does Gerbicz get included in the discoverers list, assuming it's prime95 or gpuowl that does the first PRP test, both of which implement the GEC?

[ewmayer]

Originally Posted by Madpoo

When it comes to finding a new Mersenne Prime, I guess the question about whether a probable finding is good enough to be accepted, or would the LL test be required before it's confirmed. Maybe that's similar to how we already verify a prime using different software - it's a way of ensuring there aren't any code issues or other obscure things.

A PRP test will never suffice to claim a new prime discovery - that will always require a deterministic algorithm be run and independently verified.

Originally Posted by kriesel

Very "on the money". And if there's a PRP discovery, I think it likely we confirm the PRP residue with a PRP run on different software & hardware, but the real mathematically acceptable proof will still be LL runs on different software and different hardware. In this case, does Gerbicz get included in the discoverers list, assuming it's prime95 or gpuowl that does the first PRP test, both of which implement the GEC?

Not to slight Robert G. in any way, but while the GEC is an important reliability improver for the programs using it, it is not a fundamental prime-finding algorithm, nor an actual software implementation thereof. It's an error-catching scheme, which someone actually needs to code it into an actual LL/PRP-test program. Put it this way: GIMPS doesn't give Crandall & Fagin credit in new-discovery name-lists - if anyone more should be added to such lists it should be those two, IMO. All of us who have written this type of code know there is a long list of folks upon whose ideas our work relies and any number of crucial software tools necessary for our work, but alas, you can't thank them all via discoverer credit.

[kriesel]

Originally Posted by ewmayer

Congrats-in-advance to George and GIMPS!

This would of course have to happen just after George embarks on a 10-day preholiday ocean cruise ... George leaving town remains our best predictor of a new M-prime discovery. :)

Maybe we should encourage George to travel more often.

[AG5BPilot]

Congratulations to the discover and everyone involved!

[kriesel]

Originally Posted by ewmayer

A PRP test will never suffice to claim a new prime discovery - that will always require a deterministic algorithm be run and independently verified.

Not to slight Robert G. in any way, but while the GEC is an important reliability improver for the programs using it, it is not a fundamental prime-finding algorithm, nor an actual software implementation thereof. It's an error-catching scheme, which someone actually needs to code into an actual LL/PRP-test program. Put it this way: GIMPS doesn't give Crandall & Fagin credit in new-discovery name-lists - if anyone more should be added to such lists it should be those two, IMO. All of us who have written this type of code know there is a long list of folks upon whose ideas our work relies and any number of crucial software tools necessary for our work, but alas, you can't thank them all via discoverer credit.

Point taken. The credits also don't explicitly list Lucas or Lehmer, or authors of the various factoring codes or algorithms that helped weed out so many other exponents early. I guess they could be considered lumped into the et al along with the thousands who ran composite primality tests and assorted factoring runs. Maybe candidates for a separate "Mersenne hunt hall of fame" listing though.

[preda]

Congrats! one MP every Christmas, they do look more frequent than expected, that's excellent news.

[chalsall]

Originally Posted by preda

...they do look more frequent than expected, that's excellent news.

Or, perhaps put another way, that's interesting....

[kriesel]

Originally Posted by chalsall

Or, perhaps put another way, that's interesting....

Or, not Eureka!, but Huh! That's funny... the more usual sound of impending discovery. Or it could be ominous, because if the current conjectures about frequency are close to accurate, we are now even more expectant of a relative drought, and in a much higher more computation-intensive range of exponents. I've been expecting for years, for the interval between discoveries to stretch out to 3 to 4 years. (So far I'm enjoying being wrong about that.) See https://www.mersenne.org/primes/
Then again, we're only up to about 2010 on the double checking front.