Base-2 Miller-Rabin rules.
 

Using [url=http://mersenneforum.org/showpost.php?p=156434&postcount=74]this seminal post from flouran[/url] as the basis I can now test Mersenne numbers for primeness exponentially faster than the ridiculously slow LL rubbish everyone is using now. And since, as is shown [url=http://mersenneforum.org/showpost.php?p=156472&postcount=81]here[/url] by jasonp, the odds of failure are vanishingly small (<=25%), we only need to use a single base-2 Miller-Rabin test.

And not only that, I have discovered a lot of primes that you all have previously missed (proving that the LL test is complete rubbish). In fact, so far, every number I have tested has come up as prime. I have been so lucky to pick only prime yielding exponents that I should buy some lotto tickets. So boo-yah to whoever decided to use the LL test, nyah nyah nya nyah nyah. Base-2 Miller-Rabin rules.

The Mersenne prime generating formula!
 

For all natural m>1 (2,3,4, ...) the following will always generate a Mersenne prime:

p=3*((2[sup]m[/sup]-1)/3)^FLOOR((S[sub]m-2[/sub] mod (2[sup]m[/sup]-1)+2)/(S[sub]m-2[/sub] mod (2[sup]m[/sup]-1)+0.9)-1)

where S[sub]k[/sub] is the familiar Mersenne test we all know (I shan't insult you all here by giving the formula, you already know it. ... Actually on second thought I will :evil: ...) S[sub]0[/sub] = 4 and for k > 0, S[sub]k[/sub]=S[sub]k-1[/sub][sup]2[/sup]-2

[quote=davar55;155667]Having THUS proved the RhymeOn Hypocrisy, it is THUS trivial to
generate an infinitude of Merelysane Primes, by the simple expedient
of implementing and executing the aforementioned algorithm.

Oops, my proofs and algorithms were swallowed in a gigantic,
cataclysmic, perplexing, accidental, err... dog.
I shall have to reproduce my work, which will take the better part
of a better day. But rest assured, the work speaks for itself.
It literally barks.[/quote]

My two pet dogs died many years ago, but being an adult
one can learn.

Announcement:

THERE ARE MORE THAN TWO MERSENNE PRIMES!

CALL THE MEDIAS !!!!!

--

[quote=;100935] You Lazy Bugger!!!!! You throw some snippets of already deduced information into the pool and hope Great Minds will create a Jason-Troels theorem that will allow you to predict the next 599+ Mersennes!!!! well I'm sorry I think it's totally - as Daffy said... Despicable!!!!!
QUOTE]

I wish RDS would add his obviously extensive knowledge of
math and our mersenne prime hunt to this thread. He might be
reminded of the theme and OP of this thread.

I hereby declare that I have completed testing ALL exponents above 43112609 up to 1 trillion. And they are all prime! I hereby claim myself as the first discoverer for all these Mersenne numbers. Yay for me. So now it is up to all of you to go ahead and test them as double checks and you will see I am correct.

Now, if by chance you test some exponent and find it to be composite, well, umm, sorry about that, I guess my computer had a problem. Of course when you test an exponent and it comes up prime then remember that I found it first, you are only double checking.

Please send my EFF prize cheque promptly, I badly need the money to buy lasers for my pet sharks. Thanks.

[size=1]PS: I don't care about split infinitives. So what. It was good enough for Star Trek.[/size]

A quack post forum? I'll try my best. I apologize to maths for this:

Hello, friends. I have discovered a BRAND NEW formula that generates ALL the prime numbers, and can factor any number! Of any size! Forget all that SIQS and GNFS nonsense! This revolutionary, groundbreaking new formula uses a quantum factor finding system, that can factor any number, in seconds! Here's proof!:

[CODE]Factoring 35521758706655037329971409985847961637290272425056291770375413337442193254599890856954872858888303755490991413597190923003914605026388250031026373071988344776434663687220795404506538332952545887411416685802218161811252964750257894047318469859271755414963179595143340284149328604983642681054065345068770092668341004219056998928671020209288042609778633874867832078550997655037992294206940604114003693681918733628801033517291089650588126602953091878665957670210006682675633317935750106731349522099742956456819990316789011541689732944613212806321762820310922436513108282700623627363202567663093063057978772262071936004949665809757417706238337943224153131011733071094177009039314748081661062950006881889102640380992536394708059249354495920392788285666524967148227503311123317871554176819028549862309407249906102162430722436645226386191849369737210444578833090476980693439277461026683130358402120871103086165939826930019395170443903741030778953506453011878470963408483029852174866214639483224682083310635552205084233117065223613608632727774024350516990816433358845249178295168297359614772933775182538057602125100720824864863894404309444586603611008088520474292337231...

Factors found: 714796390531060293112273373128694572048059632013845672106699367836670601586066572501750612551927748114281775493682430028815506298408427893630605439278347631029471731621259625882702636796961049357304837516393280126726566141307597869034960058913968343887190367334685761176771301575350844125435119263636127851578835298815106930044452880541406925588493824958761911635184914567535491379767687216426705655075791550319132512112515322813090158608312632185826348322378221697782642086013168894102840000122604928731724551234693977301246248678373726467819958629288660358759521292811 * 49694932958830460331032353191421138979693613874237675383624619514925110286536516395457570224678533442446072434612655962437360897690291365292897634006867719318275859730921633796239693085011172534918759318187452481135530559300297155702075786176312641123850571194369409409457281036530350593066804748135255221352902307154093809521091895508858465436054332852965432433517009946245676581079357703355984813319973961092531974741351220447205939541614527665799070259792424239652886460881697636911069228637220566830662857952927052906502234679743533469845555335509989403106968574914944802145434680166221

Elapsed time: 6.2021 seconds.
[/CODE]

The quantum factor finding system is so effective, that [B]RSA would be compromised as is today[/B]. This is why the quantum factor finding system's mechanisms remain secret.

[QUOTE]Using this seminal post from flouran as the basis I can now test Mersenne numbers for primeness exponentially faster than the ridiculously slow LL rubbish everyone is using now. And since, as is shown here by jasonp, the odds of failure are vanishingly small (<=25%), we only need to use a single base-2 Miller-Rabin test.[/QUOTE]

For one that's so quick to criticize others, you are excellent at being a kook. Have you been reading lots of kookery recently?.. Dammit, I just walked into that one.

[quote=3.14159;221722]Hello, friends. I have discovered a BRAND NEW formula that generates ALL the prime numbers, and can factor any number! Of any size! Forget all that SIQS and GNFS nonsense! This revolutionary, groundbreaking new formula uses a quantum factor finding system, that can factor any number, in seconds![/quote]

[quote=Paul Zimmermann]
Once you have solved the above challenges, to really convince me you have found an efficient factoring algorithm, please do the following: [LIST][*]pick up a large unfactored publicly known integer, say N ([URL="http://en.wikipedia.org/wiki/RSA_numbers#RSA-1024"][COLOR=#800000]RSA-1024[/COLOR][/URL] should be enough to convince me and many other people);[*]from the factorization N=pq you have, deduce the private key d = 1/e mod (p-1)(q-1) corresponding to the public key e=65537;[*]compute c = 3[sup]d[/sup] mod N;[*]send the integer c to me (or publish it on some web page);[*]on my side, I will compute m = c[sup]65537[/sup] mod N and check that m=3.[/LIST][/quote]
[URL]http://www.loria.fr/~zimmerma/records/rsa.html[/URL]

So can you factor RSA-1024 and do the instructions above?
Here's RSA-1024:
[code]RSA-1024 = 135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256239341020864383202110372958725762358509643110564073501508187510676594629205563685529475213500852879416377328533906109750544334999811150056977236890927563[/code]

:devil:

Brand new technology for Mersenne primes
 

Hello, friends. I have a REVOLUTIONARY new technology for finding MERSENNE PRIMES!

Stop using that LL garbage! That is outdated and USELESS! Try our revolutionary new method that uses consecutive division, to find super large Mersenne primes!!

The divisions take place in a very very short time! Our machines use revolutionary quantum technology to test for numbers no one has ever dreamed of testing before.. And we have found a very large Mersenne prime! We have broken a record here!!!

Here is our Mersenne prime:

2[sup]3971024427881617784446989042698959305737250294982092756939591767576453404439030489955509227409721981924650383025441722461857496719966418363269236629669728139979470828471218304117361[/sup]-1 is a prime number!!
Here is our data:

[code]Testing 2[sup]3971024427881617784446989042698959305737250294982092756939591767576453404439030489955509227409721981924650383025441722461857496719966418363269236629669728139979470828471218304117361[/sup]-1

>>Performing 12870 divisions..
>>2[sup]3971024427881617784446989042698959305737250294982092756939591767576453404439030489955509227409721981924650383025441722461857496719966418363269236629669728139979470828471218304117361[/sup]-1 is a proven prime!
Elapsed time: 0.000000000000245671 seconds.
[/code]

Also: We have made so many improvements to the factoring algorithm, that its factoring run time is:
log[SUB]1877[sup]1877[/sup][/SUB](log[SUB]1877[sup]1877[/sup][/SUB](log[SUB]1877[sup]1877[/sup][/SUB](log[SUB]1877[sup]1877[/sup][/SUB](0.00000005 * x * (1877[sup]1877[/sup] ↑↑ 4)))))

[QUOTE=Merfighters;223458][URL]http://www.loria.fr/~zimmerma/records/rsa.html[/URL]

So can you factor RSA-1024 and do the instructions above?
Here's RSA-1024:
[code]RSA-1024 = 135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256239341020864383202110372958725762358509643110564073501508187510676594629205563685529475213500852879416377328533906109750544334999811150056977236890927563[/code]

:devil:[/QUOTE]

I cannot do that, as you will steal my work! It's.. It's a CONSPIRACY! You're all out to get me, aren't you?? I'll expose you for the algorithm-thieving morons you are!! I'll expose you soon enough!! I know the truth about you and your little thieving cronies!! I won't let you ruin my discovery and hoard my credit!! I won't let you ruin my reputation!! This is obviously an attempt at algorithm thieving! I saw right through your obvious charade!!