40th Mersenne Prime Announced

[master_q 0]

On December 2, 2003 the new largest Mersenne Prime has been found!

 

2^20996011 - 1

 

(6,320,430 decimal digits)

 

 

Mersenne prime numbers is a # of the form M_n = 2ⁿ - 1

 

 

Here's a sample of what the # looks like in decimal (a very small look):

 

Click for Spoiler:

12597689545033010502049430957482431145599341608535183595225467012565498768908351

560221240096802828536132544127158323325481150465301076316712373525865122379762339

216809775290417412103179302776674988327013170222994298484439414938614146923615146

405320384930131677411867193308775658535744726248719065403711481011864235214608870

615842409469314611448863715681657029267796819632752301201087556786613770461055495

933585005892941397606910142976732340458356485482829104205410261521824675460358635

318886299052948972072378456299284969747785194967449947263357778460084073054227063

237230857386208786801217637324944607176406405201315319242434805555451075151859547

651927121451554795786023853642248011842056001818692085289670633662434434237963360

482574004972907875893795774564139846253964750557261083366582544778267753655854004

516485291984069227982534801882639875735243814139761859976740903614383300776007640

602879886776451060696950192685474337560217722801456673504766585339594202214986116

171839848399529321311217504574314623727784867403638943909356397548795460505395781

567056690146345502254952233911362464420761736131062023409653833540487998295787428

536268747609573194990589952585284058978406612371425447432039473118242332718966808

523385318546746710849171861091272207252470562642242593727097871110063852394002273

177286535115268249200180376713447682216016738872018116273341803334492004921645687

859123784269412899800784483155912339308539368668807933038384576412491897416260897

238990465481682071284158496846173252789328618622512214627650931542584898931886886

039492274475887949616084062719223538358005653738372935422217395612489591373385198

645998355370672802198211220540831165529170860779249091078198026760261418715271639

823146051357841009765921182804421467332078278639820153068805189398472900287029222

609101030332699112203653971967358352828566973911710159905429577162539180954521754

020988752410211257746635034013461597207864738708767984851946560307460134849915416

231609087243482132232052496957174116650790359084627875586064675273836290397197574

310752981277220988572746902808990793228734980082274371 . . . .

 

[The complete # saved on a HD is about 7 MB!)]

 

 

 

Another Prime # Topic: http://www.startrekfans.net/index.php?showtopic=3119

 

 

Master Q

StarTrek_Master_Q@yahoo.com

Edited December 29, 2003 by master_q

[A l t e r E g o 9]

I couldn't be more happy over the news but what's it mean? B) How will it help us?

[master_q 0]

I couldn't be more happy over the news but what's it mean?  B) How will it help us?

To a certain degree nothing (lol), but it does help us develop an understanding of Number Theory. It can help prove or disprove certain theories. And just searching for primes help mathematicians understand Number Theory. A primality test really tests that understating. If you look at the topic that I linked to it will give some more info.

 

 

Master Q

StarTrek_Master_Q@yahoo.com

Edited December 29, 2003 by master_q

[A l t e r E g o 9]

It can help prove or disprove certain theories.

 

Ahhh, that makes sense. Thanks.

[master_q 0]

It can help prove or disprove certain theories.

 

Ahhh, that makes sense. Thanks.

Well then go back to my other topic on a method to test primes made by Fermat.

 

It says - If any # “p” is a prime and any # “a” is < p, then a^(p-1) – 1 will be divisible by p

 

Example)

p =7

2^(7-1) – 1 = 63

63 is divisible by 7

 

 

2^(n-1) – 1

And in this we want to find out if n is a prime then we have to figure out if it is divisible by n. BUT even if it is divisible by n this does not mean that it must be a prime!

 

For Example) 341 is not a prime, but it is divisible into 2^340 – 1

We get a pseudoprime. Now that we looked at # 341 we now know that Fermat’s property is not always correct. It does not give us primes all the times, but can give us pseudoprimes too.

 

 

{EDIT} I found math typos

 

Master Q

StarTrek_Master_Q@yahoo.com

Edited December 29, 2003 by master_q

[A l t e r E g o 9]

B) *looks up to see what just flew over head* B)

[master_q 0]

Ummm. . . pretend we always thought the Fermat method works. Then we test the number 341. It passes the Fermat test, but after much work we find out that it is not a prime. Now after we did that we learned something new.

 

 

Master Q

StarTrek_Master_Q@yahoo.com

[A l t e r E g o 9]

pretend we always thought the Fermat method works. Then we test the number 341. It passes the Fermat test, but after much work we find out that it is not a prime. Now after we did that we learned something new.

 

Oh yeah, I've learned something: never ask a math question! But seriously, your explanation (in laymans terms) has helped bring me closer to understanding. B)

[master_q 0]

Oh yeah, I've learned something: never ask a math question! But seriously, your explanation (in laymans terms) has helped bring me closer to understanding. B)

Good to hear. It is a bit more complex, but that's one of the basic benefits.

In my other topic that I created in June/July the APRCL test is now used but the more #s we find hopefully we then can find more shortcuts in finding primes and at the same time understand the concept of number theory to a greater degree

 

 

Master Q

StarTrek_Master_Q@yahoo.com