Post B6Ds0OcbQkDA9E7r6m by linear@nya.social
(DIR) More posts by linear@nya.social
(DIR) Post #B6ANMIyxOkqcyVfXii by linear@nya.social
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one of my computers found a factor https://www.mersenne.org/report_exponent/?exp_lo=159934081
(DIR) Post #B6ANhY3mXCFHor3UaO by linear@nya.social
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i have found a few this past 48 hours, actuallyhttps://www.mersenne.org/report_exponent/?exp_lo=160174243&full=1https://www.mersenne.org/report_exponent/?exp_lo=17900093&full=1https://www.mersenne.org/report_exponent/?exp_lo=17900063&full=1
(DIR) Post #B6B5V1MmesPuvjmQnA by linear@nya.social
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i've been tuning a bunch of my machines to figure out roughly where the optimal work distribution pattern on them lies, for the best throughput over time. i don't have all of them running though and will be shutting more of them down soon for weather/heat reasons.however, my most powerful server (which is also my most power-efficient), i will probably still have doing some of this 24/7 as an idle process.
(DIR) Post #B6B5uhRnL8McgIMucy by linear@nya.social
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that server has a somewhat silly amount of RAM, on account of i managed to snag some Intel Optane DCPMMs a few months ago before the RAM prices spiked.mersenne.org tracks several types of work, with the up-front goal of the project being testing mersenne numbers to find large primes. the memory does nothing to help with this directly - the tests used (Lucas-Lehmer (LL) and Fermat Probable Prime (PRP)) do not make use of this extra RAM. however, they do not there are worktypes that will make use of it.
(DIR) Post #B6B6hcmZTM8eP2Ppb6 by linear@nya.social
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the PRP and LL tests do not tell you anything more about a given mersenne number than whether it is prime or composite (with a "residue", essentially a leftover / remainder value, that can be used to confirm the check by doing it again; or in the case of recent PRP tests, also a small proof to quickly verify without a full re-do)if you find out that a number is composite through one of these tests, you still do not know its prime factors.
(DIR) Post #B6B6n6GlGgiRIq9EDg by linear@nya.social
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Pollard's P-1 algorithm is a type of test that can make use of this RAM, and has a configurable chance of finding a factor. for mersenne numbers of interest, that chance is usually between 3% and 15% per number, depending on the bounds that it is run to - most often close to 5%. this test is usually run before LL/PRP because it is faster and knocks out many candidates with less work than a full prime test. if a second person runs a PRP test on the same number and to the same bounds, there is no additional chance of finding a factor - they will get the same result as the previous runner. doubling the RAM means you can double your effective compute, and do the same test in less time, or push your bound higher to increase your chance.
(DIR) Post #B6B7r5L8lW1FX6ezWC by linear@nya.social
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Lenstra's Elliptic Curve factorization Method (ECM) is similar to P-1. it is technically more algorithmically efficient if your goal is to find a factor, but for a wide variety of reasons, it is not used to rule out possible prime candidates like P-1 is.ECM benefits from large amounts of ram just like P-1 does, essentially using it to build a giant lookup tree to speed up calculation.unlike P-1 ECM requires an input "seed" value in the form of an elliptic curve and two points chosen on it. the chance of success of finding a factor is per seed value in ECM, so you can do ECM on the same number repeatedly, without increasing the bounds, in the hopes of eventually finding a factor.increasing the bounds does also increase the chance of finding a factor, like in P-1.this algorithm is usually used after a number is determined to be composite, by people who want to answer the question "so what are it's factors, then?"
(DIR) Post #B6B8PtdsFXFZO81QK8 by linear@nya.social
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my server having nearly 1TiB of not-quite-DDR4 (with 192GiB of DDR4 acting as L4 cache) makes it very good at P-1 and ECM.these are not only useful for hunting mersenne primes - ECM can be used for factoring anything. you could, for example, attempt to crack an RSA key with ECM. i am in fact trying to do this now on an RSA key that is ostensibly 4096-bit but has actually been intentionally crafted to be much weaker. an RSA challenge number might actually not be out of the question, but it would take this setup several years even in the perfectly optimal case, and a few decades in a more likely case.however, what i have it focusing on (balanced with other odd jobs) is ECM on M1277 (the mersenne number of the form 2^1277-1), which is the smallest mersenne number with no known factors, and M1213 (= 2^1213-1), the smallest one which is not fully factored (i.e. has at least some unknown prime factors remaining. one or more known factors may be composite). possibly also M1217.https://www.mersenne.ca/exponent/1277https://www.mersenne.ca/exponent/1213https://www.mersenne.ca/exponent/1217
(DIR) Post #B6B8s79vaT7DQ1TDbk by linear@nya.social
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i want to learn how to implement P-1 and ECM factoring myself, but i have much reading and understanding to do first
(DIR) Post #B6BAXdPmfLGJHkFVMe by linear@nya.social
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it does this while also running various other home services (and maybe soon other stuff that i want to move from cloud to this) and it does a very good job.thank you dell poweredge r640
(DIR) Post #B6BAqg2D9L8SudIr5M by linear@nya.social
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my home novell netware ipx networking lab is also currently running as a set of virtual machines on this same server.it also runs a forgejo runner, which i have set up on codeberg to use for my own projects and any codeberg organizations i am in (which is already several somehow)and i think two netbsd vms. i'm not sure why there's two of them
(DIR) Post #B6BB5bI94AV4Xus8qO by linear@nya.social
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oh and there's a smattering of little game servers in containers (minecraft, vintage story, space station 14, soon to be some quakes) that sometimes run on this and sometimes run on a xeon phi (there's migration/failover) for me and my partners and their friends.
(DIR) Post #B6BB7yRRxwHuvLM9Fw by linear@nya.social
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a home server can be a very useful thing
(DIR) Post #B6Ds0ORc5bQ9b8z4ym by zardoru@dragon.style
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@linear the average user only needs one or two servers at home. and a dns box. of course :7
(DIR) Post #B6Ds0OcbQkDA9E7r6m by linear@nya.social
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@zardoru@dragon.style i think this is unironically true, except that the manufacturers that could be making incredibly useful low-spec home servers deployed in most internet-enabled households, without even changing the hardware they are making, instead choose to create wifi router firmware