Thanks for the link.

[QUOTE=storflyt32;385718]Right now, the largest known Fermat prime is 475856^524288+1 which is a quite bit smaller number than Mersenne48 (or M48).[/QUOTE]

Hmm ... I was under the impression that 65537 is the largest known Fermat prime, but hey, what do I know?

@ ewmayer

I guess you certainly know this already.

Here is the general syntax when it comes to the Fermat numbers and their possible factorization.

2^0 + 1 = 2
2^1 + 1 = 3
2^2 + 1 = 5
2^4 + 1 = 17
2^8 + 1 = 257
2^16 + 1 = 65537

These numbers are the six first and only known Fermat factors which are known to be prime.

They are designated F(0) through F(5), respectively.

Try using for example F(6) in the input box at factordb.com (and not the web-browser address bar) and press the "Factorize!"-button.

2^32 + 1, 2^64 + 1, 2^128 +1 and 2^256 + 1, 2^512 + 1, 2^1024 + 1 and 2^2048 +1 are known to be composite numbers as a whole,
although they have now been completely factored.

But when it comes to 2^4096 + 1, 2^8192 + 1, 2^16384 + 1 and 2^32768 + 1 and so on, these numbers are only partially factored
for now, meaning that there is a mix or combination of prime factors and a remaining composite part which has yet to be factorized.

Finding the remaining factors of these numbers apparently is not a trivial manner. First a factor which is somewhere between 54 digits

(P54 = 568630647535356955169033410940867804839360742060818433)

and less than about

(2^4096+1)/25860116183332395113497853167940236083358054650286886725246241569916604094012679963198712829716480001

(which is the syntax for the C1133),

has to be found and it needs to be divisable from both 2^4096+1 and the C1133 mentioned above in order to become a valid factor.

The question becomes - in which way is this supposed to be working?

For now I really don't know the answer to this question and I have tried it out a couple of times.

Here is another example:

[URL]http://factordb.com/index.php?query=3059328257448451012124528914924445459289472845506271570768416772257721865362447461948849641168439486188201742608695176185034167120620937263286034904233584751954360912650820750922532773634896817894712355879514579840739[/URL]


The factors are already individually known, but apparently some 76.5 hours more to go in order to possibly factorize this number:

Here are the factors for this number:

P46 = 7774289568841054467342907020273258993552032567

P171 = 39351869136828636825562309706971225245700129962404540849168691727314561178481864067
5586069862814412735711970194801864005631730155162613125109843290448727462456016513851317

[QUOTE=storflyt32;386329]@ ewmayer

I guess you certainly know this already.[/QUOTE]
Do you realise who you are talking to?

[QUOTE]Here is the general syntax when it comes to the Fermat numbers and their possible factorization.

2^0 + 1 = 2
2^1 + 1 = 3
2^2 + 1 = 5
2^4 + 1 = 17
2^8 + 1 = 257
2^16 + 1 = 65537

These numbers are the six first and only known Fermat factors which are known to be prime.

They are designated F(0) through F(5), respectively.[/QUOTE]It really isn't a good idea to start inventing your own notation. You should use the standard terminology and then everyone will know what you are talking about.

The numbers in your list above, with the exception of the first one, are Fermat numbers (not Fermat factors).
Remove the first one which does not belong in the list, then the remaining numbers are [TEX]F_0[/TEX] through [TEX]F_4[/TEX]. The Fermat number [TEX]F_n[/TEX] is [TEX]2^2^n+1[/TEX].

Sorry, should have skipped the 2.

BTW: Was replying to ewmayer. Should be readily visible.

Anyway, I now have the output here for the mentioned 7333*2^138560+1 .

If this number was a prime number, it should definitely be showing up, but it does not do so.

What if I update the factordb with the most recent result and let you know?

Edit: And this is something which I am apparently not able to do.

Trust the numbers (meaning results).

[QUOTE=storflyt32;386345]Anyway, I now have the output here for the mentioned 7333*2^138560+1 .

If this number was a prime number, it should definitely be showing up, but it does not do so.

What if I update the factordb with the most recent result and let you know?

Edit: And this is something which I am apparently not able to do.

Trust the numbers (meaning results).[/QUOTE]

Output from what? Show up where? What recent result?
Your comments are so general that it's hard to figure out what you are talking about, trying to do, or not understanding from the lengthy advice you have been given in this thread.
The number you refer to is prime, and has been known to be prime for a while- so there is nothing to update in factordb or anywhere else. You have discovered nothing new about this number, but you have surely discovered which tools don't work for numbers this size.

[QUOTE=storflyt32;386329]@ ewmayer[/QUOTE]
[URL]http://www.ams.org/journals/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.pdf[/URL]

:whistle:

[QUOTE=storflyt32;386329]@ ewmayer

I guess you certainly know this already.[/QUOTE]Yeah, exactly. I doubt ewmayer could tell the difference between Pépin's test and a pregnancy test. You tell him dude. :boxer:

Thank you very much!

Including [URL]http://factordb.com/index.php?query=3289018909828839950285397233495375495312608729711519999908385629462589823501707053451816348898028195709146280381194398910952848236577722255912280830117106073745410924257454722225416180933818531872928654602163702255020504550525896713971683343306725862850881[/URL]


Reading the .pdf right now, by the way.

You do not have to post or update this one if you wish not to do so, but this number:

[URL]http://factordb.com/index.php?query=10543858099141793567633706165613456571488994021324464032184255388501735734830314244716706835906749187785349381054183287392145341367842938953708368214292103334328105248332619908403542418842578894856690780599845067603784321027354628942698284377316441276634934880201623667710496773929693357694193269051422249268025368211692151585189681074812700784597020009094761047486927562009119226854561099845456510080977130753090111834123396116614031339670717428868049615591632090459747677046286964578601983401366511046242168546147768383690899516261551099472238446079243800103410549239830923104465229408541903281612612851226720768200137636245559187801381888198683544007019417707419456721148906013839302279348089558110191155943197067173948849807156235238157662844920262390207716107361825364483070705440058534429259974094029475525202297663281509918939435399944237755058601170817571788095655119835981550745773303862840478605165095551231145272355473159791462857543343159034190018602967650306257601279230308480192009040129237[/URL]


has then the two factors

[URL]http://factordb.com/index.php?query=393518691368286368255623097069712252457001299624045408491686917273145611784818640675586069862814412735711970194801864005631730155162613125109843290448727462456016513851317[/URL]

and

[URL]http://factordb.com/index.php?query=26793792341807736634989996206703221928991974551245243656608357295705957662434910993643582652735889417114477578195143305386606165633460494479352618199027436253125675855298638156898862031234291454088819107336178258992586290735281701539436654426222016224877857981627455730618970402046410998073275965537433922830595878994170968342869032386464859697352301955142765924502144312285624617397751070093352625339376546895701802356390969877934653964801145307320505921478365986799435114748798120051403951756511452487507878545576504672167732467680117932062327299154686527365885435933234831102575520705134772227077571687294915880830214822585884390631938094801973796975327038072799759540642174453561362916450601573932599514869012246747271586372225973769612485189642375073189717303788897993289702939522295629255121309853562659549833018243089817881761[/URL]

respectively.