Mersenne non-primes

2003-12-27, 14:14

Is there a list anywhere of the Mersenne numbers known not to be prime?

patrik · 2003-12-27, 14:51

At the bottom of the status page
http://www.mersenne.org/status.htm
there are links to different files making up the Mersenne database. The first three (exponents of factored numbers, double-checked numbers and numbers that have had only one Lucas-Lehmer test) would be what you are asking for.

Historically there has been an error rate of a few percent in the Lucas-Lehmer tests. Therefore the computation is repeated. The third file above can contain more than one test for an exponent if the tests are not matching.

GP2 · 2003-12-27, 17:37

Quote:

Originally posted by Unregistered
Is there a list anywhere of the Mersenne numbers known not to be prime?

You can get this by combining the list of exponents with known factors (factors.zip) and the list of exponents that have had two Lucas-Lehmer tests with matching 64-bit residues (lucas_v.zip).

Currently 2,667,859 exponents have known factors and 256,339 exponents have two matching LL tests.

dswanson · 2003-12-27, 17:40

Strictly speaking, the third file (hrf3.txt) doesn't meet the criterion "known not to be prime". Each number in this file has been LL tested once, and for each number the result of that LL test indicates that the number is not prime. But until the LL test is repeated (doublecheck) and it is confirmed that the doublecheck result matches the first result, it cannot be stated for certain that the number is not prime. Until the doublecheck is complete, it's possible that the first LL test was incorrect.

2004-01-03, 16:41

The main reason for my interest was that I thought it would be a neat objective test for anyone claiming supernatural or extraterrestrial knowledge. The factors of an unknown Mersenne Prime is hardly disruptive knowlegde: but if they really came back with one, they'd be worth taking seriously. Much more likely, they'd not come back at all, or come back with an answer that was demonstrably wrong.

I'm not qualified to produce such a list, nor to protect my home computer from the sort of hassle that it would attract if it attracted interest. Is there someone out there who feels like taking it up?

GP2 · 2004-01-03, 17:14

Don't forget that knowing a number is not prime is not the same as actually knowing its factors.

For instance, we know that M971 is not prime because it fails the Lucas-Lehmer test, but we currently don't know any factor for it.

A good test of extraterrestrial intelligence would be if they could tell us what, say, M45 is...

lpmurray · 2004-01-04, 03:17

Quote:

Originally posted by GP2
Don't forget that knowing a number is not prime is not the same as actually knowing its factors.

For instance, we know that M971 is not prime because it fails the Lucas-Lehmer test, but we currently don't know any factor for it.

A good test of extraterrestrial intelligence would be if they could tell us what, say, M45 is...

I know this is off the point you were making about m971 but your statement about no known factors got to me and I tried to use the ecm part of prime95 for the first time. My results file said this...

[Sat Jan 03 20:52:46 2004]
UID: lmurray/hp2200, M971 is not prime. Res64: F366174A235BF2B2. WZ1: 11540C62,504,00000000
UID: lmurray/hp2200, M971 no factor to 2^40, WZ1: 00100004
[Sat Jan 03 20:58:58 2004]
ECM found a factor in curve #1, stage #1
Sigma=8727776697676685, B1=1000000, B2=100000000.
UID: lmurray/hp2200, P971 has a factor: 495211
[Sat Jan 03 21:04:04 2004]
ECM found a factor in curve #4, stage #2
Sigma=8252620261253466, B1=1000000, B2=100000000.
UID: lmurray/hp2200, P971 has a factor: 3019967621847401
[Sat Jan 03 21:10:21 2004]
ECM found a factor in curve #10, stage #2
Sigma=905319878861278, B1=1000000, B2=100000000.
UID: lmurray/hp2200, P971 has a factor: 745797773625002825025979

Does this mean we now know factors for it or am I not understanding this?

nfortino · 2004-01-04, 03:26

What you have is P971, meaning 2⁹⁷¹+1. We are looking for factors of M971, of which none are known.

Note: P971=3*495211*3019967621847401*745797773625002825025979*P205 (a 205 digit prime).

lpmurray · 2004-01-04, 03:59

Thanks for the answer. I got the part that the 971 I was using is the 2⁹⁷¹-1. I guess my problem is I don't understand what m971 is, and how you would go about looking for a factor for this. Thanks for any and all education... Although I've always loved math, it doesn't feel the same about me when it comes to understanding it

nfortino · 2004-01-04, 05:39

For a good understandable explanation of the math behind the project, look here at the math page of the GIMPS website. There is also a Mersenne page here at The Prime Pages (a site you will probably want to explore.)

dsouza123 · 2004-01-04, 17:00

Could Prime95 if it allowed composite exponents be used to find factors, or is there some mathematical issue that precludes it ?

What about the power mod function is that valid for mersenne composites ? Would the factors still be in the form 2kp+1 ?

2004-01-03, 16:41	#5
Gwydion 3,343 Posts	Thanks for the answers The main reason for my interest was that I thought it would be a neat objective test for anyone claiming supernatural or extraterrestrial knowledge. The factors of an unknown Mersenne Prime is hardly disruptive knowlegde: but if they really came back with one, they'd be worth taking seriously. Much more likely, they'd not come back at all, or come back with an answer that was demonstrably wrong. I'm not qualified to produce such a list, nor to protect my home computer from the sort of hassle that it would attract if it attracted interest. Is there someone out there who feels like taking it up?

2004-01-04, 03:26	#8
nfortino Nov 2003 3×5×11 Posts	What you have is P971, meaning 2⁹⁷¹+1. We are looking for factors of M971, of which none are known. Note: P971=34952113019967621847401745797773625002825025979P205 (a 205 digit prime). Last fiddled with by nfortino on 2004-01-04 at 03:30

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2003-12-27, 14:14	#1
Unregistered 2·479 Posts	Mersenne non-primes Is there a list anywhere of the Mersenne numbers known not to be prime?

2003-12-27, 14:51	#2
patrik "Patrik Johansson" Aug 2002 Uppsala, Sweden 5²×17 Posts	At the bottom of the status page http://www.mersenne.org/status.htm there are links to different files making up the Mersenne database. The first three (exponents of factored numbers, double-checked numbers and numbers that have had only one Lucas-Lehmer test) would be what you are asking for. Historically there has been an error rate of a few percent in the Lucas-Lehmer tests. Therefore the computation is repeated. The third file above can contain more than one test for an exponent if the tests are not matching.

2003-12-27, 17:40	#4
dswanson Aug 2002 2³·5² Posts	Strictly speaking, the third file (hrf3.txt) doesn't meet the criterion "known not to be prime". Each number in this file has been LL tested once, and for each number the result of that LL test indicates that the number is not prime. But until the LL test is repeated (doublecheck) and it is confirmed that the doublecheck result matches the first result, it cannot be stated for certain that the number is not prime. Until the doublecheck is complete, it's possible that the first LL test was incorrect.

2004-01-03, 17:14	#6
GP2 Sep 2003 A19₁₆ Posts	Don't forget that knowing a number is not prime is not the same as actually knowing its factors. For instance, we know that M971 is not prime because it fails the Lucas-Lehmer test, but we currently don't know any factor for it. A good test of extraterrestrial intelligence would be if they could tell us what, say, M45 is...

2004-01-04, 03:59	#9
lpmurray Sep 2002 89 Posts	Thanks for the answer. I got the part that the 971 I was using is the 2⁹⁷¹-1. I guess my problem is I don't understand what m971 is, and how you would go about looking for a factor for this. Thanks for any and all education... Although I've always loved math, it doesn't feel the same about me when it comes to understanding it

2004-01-04, 05:39	#10
nfortino Nov 2003 165₁₀ Posts	For a good understandable explanation of the math behind the project, look here at the math page of the GIMPS website. There is also a Mersenne page here at The Prime Pages (a site you will probably want to explore.)

2004-01-04, 17:00	#11
dsouza123 Sep 2002 2·331 Posts	Could Prime95 if it allowed composite exponents be used to find factors, or is there some mathematical issue that precludes it ? What about the power mod function is that valid for mersenne composites ? Would the factors still be in the form 2kp+1 ?