41st Known Mersenne Prime Reported!!

[jinydu]

When I look at a graph, the ratio between successive Mersenne prime exponents doesn't seem to be closing in on a limiting value, at least not for the first 38 exponents.

Huh ? Wha?
Did you see the link I gave ya. That's dead on the money.
Well as far as prime numbers are concerned anyway.

Do you mean closing in on a rational limiting value? ie, 3/2
Or irrational limiting value? ie, 1.47576

Well if you meant rational, then ofcourse not.
If you mean irrational, then I suggest you are. (In a nice manner)

[jinydu]

Here is the graph I made using Microsoft Excel. The first point is (1, 3/2), the second is (2, 5/3) all the way up to (37, 6972593/3021377). As can be seen, the points don't seem to be closing in on a limiting value towards the right-end of the graph.

[AP]

Hi all,

what about the verification of (probably) M41? Is it already on its way?

Regards
Achim

jinydu
Here is the graph I made using Microsoft Excel. The first point is (1, 3/2), the second is (2, 5/3) all the way up to (37, 6972593/3021377). As can be seen, the points don't seem to be closing in on a limiting value towards the right-end of the graph.

As far as prime numbers are concerned, that's close
If you take the average of all, it comes out to be about 1.99.
But take the average of the first 8, or the first 11 Mp, = 1.47... ,

You are right about this though, there is not enough data to do accumulative averages acurately.

Edit: I ran the averages, and it tends to get smoother as n gets large, but when it's rough it really rough. This is due to prime number divergence.

[Xyzzy]

Originally Posted by AP

what about the verification of (probably) M41? Is it already on its way?

Yes...

[Prime95]

Xyzzy started a P4 verification soon after the prime was found and has completed 5 million iterations.

Ernst started a run using mlucas on a single-cpu system on Sunday. He estimates 3 1/2 weeks to complete the run. He is at 1 million iterations.

Jeff in Canada started a Glucas run Monday on an 8-way Alpha box. He too is at 1 million iterations and matches Ernst's interim residue. If CPU loads stay low Jeff could finish in just over two weeks.

Tony in France also started a Glucas run Monday but ran into some threading problems. His multi-CPU Sun box hasn't reached 1 million iterations yet. However, he going to try and switch to a 16-CPU Itanium machine. No estimates on a possible completion date.

Mike, Ernst, and I will post progress as it comes in. Keep your fingers crossed!

[Jeff Gilchrist]

Its actually a 16-way Alpha box but its shared amongs researchers so I think they are limiting the number of CPUs you can run. I'm actually just using 4 CPUs (that seems to be the max) with GLUCAS but getting pretty good speed.

Lets just hope the queue software is smart enough not to overload the system (ideally it should only let enough processes/threads run for the # of CPUs the box has) so lets hope the load doesn't go up.

Jeff "in Canada" Gilchrist

[PrimeCruncher]

Originally Posted by wpolly

Could anyone post the 4 candidate exponents along with their residue?

Well, GP2 did last time, so I guess I'll do the honors this time. The four remaining possibilities based on the various info posted in this thread:

21169397		0x746B874910048A__	curtisc	 grn16-11
22776563		0xCF3C3B04BD5A10__	curtisc	 wde3100-028
24036583		0x7EC80125B6DB7E__	jfindley M3	
23393483		0xD9BFF123AAE613__	mesirow	 DellH

[Xyzzy]

6,000,000...

[jinydu]

Originally Posted by PrimeCruncher

Well, GP2 did last time, so I guess I'll do the honors this time. The four remaining possibilities based on the various info posted in this thread:

21169397		0x746B874910048A__	curtisc	 grn16-11
22776563		0xCF3C3B04BD5A10__	curtisc	 wde3100-028
24036583		0x7EC80125B6DB7E__	jfindley M3	
23393483		0xD9BFF123AAE613__	mesirow	 DellH

But all of them have a non-zero residue.