Mersenne number factored (disbelievers are biting elbows)

alpertron · 2014-06-02, 11:32

Using http://www.mersenne.ca/prp.php , I reserved 1000 Mersenne composite numbers in order to perform PRP on the cofactors.

My computer found that:

M1304983 = 52199321 x PRP-392832

The log from Prime95 is:

[Mon Jun 02 04:50:39 2014]
M1304983/52199321 is a probable prime! We1: D4B7573A,00000000

It appears to be the largest PRP known from Mersenne numbers.

PS: Doing a search on Internet, I found that this PRP was already done:
PRP top records

Anyway I will continue performing more PRPs on Mersenne number cofactors.

bloodIce · 2014-06-02, 20:08

It is a pity that this PRP has been reported before, but good luck with the rest. I was doing PRP on cofactors for for a while. Absolutely stupid many would say, but it is funny and anything above the current is a record holder :-).

Batalov · 2014-06-02, 20:47

It would be, in theory. That is, if one knew exactly how far Never-Odd-Or-Even already went. Because you don't know, it is a high risk-low return type of research project. The PRP test time goes up, up and up, and the probability of the cofactor being prime goes down and down. You also don't know whether NOOE is still running his tests; if he actually is, then you are virtually attempting to catch up with a power player with significant resources (or in other words, you are not going to catch up).

alpertron · 2014-06-02, 21:01

Well, this is not entirely correct, as several new prime factors of Mersenne numbers with exponents lower than 2M are being found every day. So I expect that they have not ran PRP on the new cofactors.

Batalov · 2014-06-02, 21:24

There is some window in this new pool, I agree.

MatWur-S530113 · 2014-06-03, 02:14

Quote:

Originally Posted by alpertron

Well, this is not entirely correct, as several new prime factors of Mersenne numbers with exponents lower than 2M are being found every day. So I expect that they have not ran PRP on the new cofactors.

I'm not sure about this. Some time ago I run ecm-curves on M-numbers without known factors in different ranges only to get candidates for a prp-test, my own best one (#2 at that list...) should be such a candidate. Only if the known factors are found definetely by TF I would do a prp-test.

Your main problem seems to be of problem of reporting a PRP-result to GIMPS (mersenne.org). As mersenne.ca seems to be 'only' a mirror it doesn't know of the prp-result, because it is not stored at GIMPS. (typically an answer like

Quote:

Sending result to server: UID: Wurtinger/i5-4670K, M4206583/322661843389993 is not prime. RES64: A51241E89B25CD16. We4: AE62110B,00000000

PrimeNet error 45: Invalid result type
ar: invalid result type: 150

will appear in communication thread and prime.log. )
But mersenne.ca works fine if the results are posted there. I assigned 4 hours ago the first 40 available exponents for prp-test at range 2M+. the tests needed 3 hours, then I simply copied the results-lines of results.txt (incl. Timestamps) and posted them at mersenne.ca resultpage. It was shown that they were added as 'not-prp' to the db and a new list of the available exponents for the same range doesn't show these exponents anymore.
So it seems to be only a problem of 'filling-up' the db at mersenne.ca. As Batalov said, it would be helpful if the results of some power players could be added, but on the other hand every new factor 'forces' a new prp-test.
But I like the idea of a prp-db

, I think I will spend some more time for prp-test in the next future.

greetings,

Matthias

bloodIce · 2014-06-03, 07:22

When I was looking for PRP, what I did was massive attack of some exponent with TF/Pminus1/ECM until it starts to be unreasonable. Unreasonable is subjective and depends on resources you have. If there were new factors, I was doing a PRP test. If there were no factors, at least I report the TF results to GIMPS (if the expo is unfactored) and Pminus1 results to mersenne.ca, ECM is never a loss. I think the chance for a new PRP is in finding new factors in the range 1.5M-3M. That range is still accessible for all methods. I should admit that the best method there is Pminus1, but ECM still kicks some factors.

alpertron · 2014-06-03, 11:38

In 4 days I cleared more than 1000 exponents in http://www.mersenne.ca and my idea is to have all the exponents below 2M with PRP done. There are still 3000 exponents to be PRP'ed to reach that goal.

bloodIce · 2014-06-03, 11:54

That is ambitious goal, but achievable. In two weeks you might be done. I may join on over 2M for a while :-). However I can do several per day, so my chances are null. Good luck, I would love to see new PRP over the current record.

alpertron · 2014-06-03, 18:45

At this moment all exponents below 1911000 were tested.

alpertron · 2014-06-04, 01:22

I found that there are some holes in the PRP database on http://www.mersenne.ca. For example, from the link: http://www.mersenne.ca/prp.php?show=...ponent=1911149 we can find a lot of exponents without PRP done, but this range cannot be reserved using the form http://www.mersenne.ca/prp.php?show=...ponent=1911149

2014-06-02, 11:32	#1
alpertron Aug 2002 Buenos Aires, Argentina 2×761 Posts	Mersenne number factored (disbelievers are biting elbows) Using http://www.mersenne.ca/prp.php , I reserved 1000 Mersenne composite numbers in order to perform PRP on the cofactors. My computer found that: M1304983 = 52199321 x PRP-392832 The log from Prime95 is: [Mon Jun 02 04:50:39 2014] M1304983/52199321 is a probable prime! We1: D4B7573A,00000000 It appears to be the largest PRP known from Mersenne numbers. PS: Doing a search on Internet, I found that this PRP was already done: PRP top records Anyway I will continue performing more PRPs on Mersenne number cofactors. Last fiddled with by alpertron on 2014-06-02 at 11:44

2014-06-03, 07:22	#7
bloodIce Feb 2010 Sweden 173 Posts	When I was looking for PRP, what I did was massive attack of some exponent with TF/Pminus1/ECM until it starts to be unreasonable. Unreasonable is subjective and depends on resources you have. If there were new factors, I was doing a PRP test. If there were no factors, at least I report the TF results to GIMPS (if the expo is unfactored) and Pminus1 results to mersenne.ca, ECM is never a loss. I think the chance for a new PRP is in finding new factors in the range 1.5M-3M. That range is still accessible for all methods. I should admit that the best method there is Pminus1, but ECM still kicks some factors. Last fiddled with by bloodIce on 2014-06-03 at 07:56

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2014-06-02, 20:08	#2
bloodIce Feb 2010 Sweden 173 Posts	It is a pity that this PRP has been reported before, but good luck with the rest. I was doing PRP on cofactors for for a while. Absolutely stupid many would say, but it is funny and anything above the current is a record holder :-).

2014-06-02, 20:47	#3
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10011110110101₂ Posts	It would be, in theory. That is, if one knew exactly how far Never-Odd-Or-Even already went. Because you don't know, it is a high risk-low return type of research project. The PRP test time goes up, up and up, and the probability of the cofactor being prime goes down and down. You also don't know whether NOOE is still running his tests; if he actually is, then you are virtually attempting to catch up with a power player with significant resources (or in other words, you are not going to catch up).

2014-06-02, 21:01	#4
alpertron Aug 2002 Buenos Aires, Argentina 1522₁₀ Posts	Well, this is not entirely correct, as several new prime factors of Mersenne numbers with exponents lower than 2M are being found every day. So I expect that they have not ran PRP on the new cofactors.

2014-06-02, 21:24	#5
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 5·19·107 Posts	There is some window in this new pool, I agree.

2014-06-03, 11:38	#8
alpertron Aug 2002 Buenos Aires, Argentina 2·761 Posts	In 4 days I cleared more than 1000 exponents in http://www.mersenne.ca and my idea is to have all the exponents below 2M with PRP done. There are still 3000 exponents to be PRP'ed to reach that goal.

2014-06-03, 11:54	#9
bloodIce Feb 2010 Sweden 173 Posts	That is ambitious goal, but achievable. In two weeks you might be done. I may join on over 2M for a while :-). However I can do several per day, so my chances are null. Good luck, I would love to see new PRP over the current record.

2014-06-03, 18:45	#10
alpertron Aug 2002 Buenos Aires, Argentina 2×761 Posts	At this moment all exponents below 1911000 were tested.

2014-06-04, 01:22	#11
alpertron Aug 2002 Buenos Aires, Argentina 2×761 Posts	I found that there are some holes in the PRP database on http://www.mersenne.ca. For example, from the link: http://www.mersenne.ca/prp.php?show=...ponent=1911149 we can find a lot of exponents without PRP done, but this range cannot be reserved using the form http://www.mersenne.ca/prp.php?show=...ponent=1911149