M40, what went wrong? - Page 3

trif · 2003-06-03, 05:43

I think we need to blame M40 on Xyzzy. I arrived a bit late for the chat on the 24th/25th, and he tells me I just missed George with exciting news--M40 had been found! Of course, after he's done yanking my leg, Tasuke comes in and Xyzzy goes even farther, saying it's an 8M found on a triple check.

Spooky having the real M40 show up a few days later.

Xyzzy · 2003-06-03, 07:43

I'm still waiting for M38½...

:(

ewmayer · 2003-06-03, 16:21

Quote:

Originally Posted by Xyzzy

I'm still waiting for M38½...

:(

So is Curt Noll, propounder of the (now-discredited) "Island Theory" for the occurrence of M-primes.

rogue · 2003-06-03, 16:42

And just as Richard Brent's search for Primitive Trimorials is nearing completion for M6972593 (after nearly 2 1/2 years) so M13466917 could be started, someone has to go and find another Mersenne prime...

flava · 2003-06-03, 18:36

Quote:

Originally Posted by ewmayer

Quote:

Originally Posted by Xyzzy

I'm still waiting for M38½...

:(

So is Curt Noll, propounder of the (now-discredited) "Island Theory" for the occurrence of M-primes.

Could you please explain us what this "Island Theory" is?

Prime95 · 2003-06-03, 20:52

Quote:

Originally Posted by rogue

And just as Richard Brent's search for Primitive Trimorials is nearing completion for M6972593 (after nearly 2 1/2 years) so M13466917 could be started, someone has to go and find another Mersenne prime...

Ernst has informed me the new Mersenne prime has no primitive trinomials. The exponent is 5 mod 8.

And 13466917 is 5 mod 8 too.

See http://web.comlab.ox.ac.uk/oucl/work/richard.brent/trinom.html for the primitive trinomials search.

So.... GIMPS needs to work a little harder to find a 1 or 7 mod 8 Mersenne prime or Richard Brent's project will come to an end!

ewmayer · 2003-06-04, 00:10

Quote:

Originally Posted by flava

Quote:

Originally Posted by ewmayer

Quote:

Originally Posted by Xyzzy

I'm still waiting for M38½...

:(

So is Curt Noll, propounder of the (now-discredited) "Island Theory" for the occurrence of M-primes.

Could you please explain us what this "Island Theory" is?

The "Island Theory" (I put the name in quotes because it was never formalized in any fashion like is typical for a mathematical theorem) basically states that M-prime exponents tend to occur in dense clusters, I believe (correct me if I'm wrong, anyone) Noll also posited that pairs were the most common type of clump, or "island" as he called it.

AFAIK Noll never made a precise definition of "clumpiness," nor has anyone provided any convincing evidence that a random selection of primes having the same overall statistical frequency and properties (e.g. the way in which they thin out as they get larger, which *can* be accurately described using statistics about the number of possible prime divisors of the prime-exponent Mersenne numbers) should on average be significantly less "clumpy" than the known Mersenne prime exponents. All the evidence we have points to the exponents occurring randomly, but with definite statistical properties, much like the (generic) prime numbers themselves.

andi314 · 2003-06-04, 11:33

Does anyone know the exponent of the "new" prime????
Thank andi314

AP · 2003-06-04, 11:46

Yes, at least George Woltman, EW Mayer and the discoverer!

But they are not going to tell us until the verification is done.

We all have to wait about 2 1/2 weeks......

Regards
Achim

andi314 · 2003-06-04, 12:06

Thanks for your answer
Andi314

nitro · 2003-06-04, 22:49

Quote:

Originally Posted by andi314

Does anyone know the exponent of the "new" prime????
Thank andi314

Yes. Don't ask. Because I found M2976221 to be prime.

View Poll Results: Where is the new (maybe not) prime?
18.0-19.0 M	3	2.11%
19.0-20.0 M	7	4.93%
20.0-21.0 M	11	7.75%
21.0-22.0 M	10	7.04%
Elsewhere, missed in DC, below 18 M	10	7.04%
14.4kbps or less to 19.2kbps	2	1.41%
21.6kbps to 26.4kbps	1	0.70%
28.8kbps to 36.0kbps	3	2.11%
38.4kbps to 52.8kbps	14	9.86%
better than dialup	37	26.06%
Less than 16 million	13	9.15%
16 million	5	3.52%
17 million	5	3.52%
18 million	9	6.34%
19 million or more	12	8.45%
Voters: 142. You may not vote on this poll

2003-06-04, 11:33	#30
andi314 Nov 2002 2·37 Posts	40th mersenne prime Does anyone know the exponent of the "new" prime???? Thank andi314

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2003-06-03, 05:43	#23
trif Aug 2002 2·101 Posts	I think we need to blame M40 on Xyzzy. I arrived a bit late for the chat on the 24th/25th, and he tells me I just missed George with exciting news--M40 had been found! Of course, after he's done yanking my leg, Tasuke comes in and Xyzzy goes even farther, saying it's an 8M found on a triple check. Spooky having the real M40 show up a few days later.

2003-06-03, 07:43	#24
Xyzzy "Mike" Aug 2002 2⁵×257 Posts	I'm still waiting for M38½... :(

2003-06-03, 16:42	#26
rogue "Mark" Apr 2003 Between here and the 18CB₁₆ Posts	And just as Richard Brent's search for Primitive Trimorials is nearing completion for M6972593 (after nearly 2 1/2 years) so M13466917 could be started, someone has to go and find another Mersenne prime...

2003-06-04, 11:46	#31
AP Sep 2002 2×7 Posts	Yes, at least George Woltman, EW Mayer and the discoverer! But they are not going to tell us until the verification is done. We all have to wait about 2 1/2 weeks...... Regards Achim

2003-06-04, 12:06	#32
andi314 Nov 2002 112₈ Posts	Thanks for your answer Andi314