What is the largest prime number ever?

vbimport

#1

Or let me rephrase it, is there a largest prime number?


#2

http://www.digitalamit.com/blog/blog/5.html


#3

3


#4

wrong isadore…yours was dated may 2004…
http://www.mersenne.org/prime.htm Feb 2005


#5

220,996,011-1


#6

Not 3 then???


#7

:bigsmile:


#8

Correct, as always. :iagree:


#9

no to put it bluntly there is not a largest prime number its like counting there is not a largest number cos when you add 1 it gets bigger so basically numbers go to infinity and so will the largest prime number
:o OMG this is getting boring time to move on i think :rolleyes:


#10

Well, I guess that answers the question.


#11

That’s hardly a proof :slight_smile: A trivial proof ad absurdum goes like this : suppose
there’s indeed a largest prime number n. Then consider the number obtained
by multiplying all primes smaller or equal to n, then add one to it. None of the
primes up to n divides this number, thus it is also a prime. This number is also
larger than n, thus n was not the biggest prime -> game over.


#12

Euh, I think you’re wrong (never thought I would say that to you).

Who says that the number obtained by multiplying those primes + 1 isn’t divisible by 2 or 3 or 4??

I mean (3571113)+1=15016 This is divisible by 2, 4,…

Or am I misunderstanding you?


#13

1


#14

This man speaks the truth!


#15

2 is prime in my book :slight_smile:


#16

Yup


#17

Here is a list of the top 100 largest prime numbers Got it here

1 2^25964951-1 7816230 G8 2005 Mersenne 42?
2 2^24036583-1 7235733 G7 2004 Mersenne 41?
3 2^20996011-1 6320430 G6 2003 Mersenne 40?
4 2^13466917-1 4053946 G5 2001 Mersenne 39
5 284332^7830457+1 2357207 SB7 2004
6 2^6972593-1 2098960 G4 1999 Mersenne 38
7 5359
2^5054502+1 1521561 SB6 2003
8 2^3021377-1 909526 G3 1998 Mersenne 37
9 2^2976221-1 895932 G2 1997 Mersenne 36
10 1372930^131072+1 804474 g236 2003 Generalized Fermat
11 1361244^131072+1 803988 g236 2004 Generalized Fermat
12 1176694^131072+1 795695 g236 2003 Generalized Fermat
13 572186^131072+1 754652 g0 2004 Generalized Fermat
14 32^2478785+1 746190 g245 2003
Divides Fermat F(2478782), GF(2478782,3), GF(2478776,6),
GF(2478782,12)
15 130816^131072+1 670651 g308 2003 Generalized Fermat
16 3
2^2145353+1 645817 g245 2003
Divides Fermat F(2145351), GF(2145351,3), GF(2145352,5),
GF(2145348,6), GF(2145352,10), GF(2145351,12)
17 62722^131072+1 628808 g308 2003 Generalized Fermat
18 212^1830919+1 551163 g279 2004
19 19502212^65536+1 477763 p160 2005 Generalized Fermat
20 13
2^1499876+1 451509 g267 2004
Divides GF(1499875,3)
21 72^1491852+1 449094 p166 2005
Divides GF(1491851,6)
22 2232007
2^1490605-1 448724 L4 2003
23 212^1421741+1 427989 g279 2005
24 149797
2^1414137-1 425703 L105 2005
25 2^1398269-1 420921 G1 1996 Mersenne 35
26 1920892^1395688-1 420150 L49 2004
27 241489
2^1365062+1 410930 L101 2005
28 1828502^65536+1 410393 GF2 2005 Generalized Fermat
29 1540550^65536+1 405516 GF2 2003 Generalized Fermat
30 1483076^65536+1 404434 GF2 2003 Generalized Fermat
31 1478036^65536+1 404337 GF2 2002 Generalized Fermat
32 547672^1337287+1 402569 SB5 2002
33 1374038^65536+1 402260 GF3 2003 Generalized Fermat
34 1361846^65536+1 402007 GF3 2002 Generalized Fermat
35 1266062^65536+1 399931 g295 2002 Generalized Fermat
36 5
2^1320487+1 397507 g55 2002
Divides GF(1320486,12)
37 1057476^65536+1 394807 g197 2002 Generalized Fermat
38 1024390^65536+1 393902 g299 2003 Generalized Fermat
39 857678^65536+1 388847 GF0 2002 Generalized Fermat
40 843832^65536+1 388384 GF0 2001 Generalized Fermat
41 1388472^1283793-1 386466 L2 2003
42 5
2^1282755+1 386149 g55 2002
Divides GF(1282754,3), GF(1282748,5)
43 671600^65536+1 381886 g55 2002 Generalized Fermat
44 252^1258562+1 378867 g279 2004 Generalized Fermat
45 2^1257787-1 378632 SG 1996 Mersenne 34
46 80857169
2^1251076-1 376620 L10 2004
47 549868^65536+1 376194 g295 2003 Generalized Fermat
48 544118^65536+1 375895 g295 2002 Generalized Fermat
49 212^1240067+1 373299 g279 2004
50 3
2^1232255-1 370947 L30 2004
51 440846^65536+1 369904 GC1 2002 Generalized Fermat
52 252^1211488+1 364696 g279 2005
Generalized Fermat, divides GF(1211487,12)
53 357868^65536+1 363969 g266 2003 Generalized Fermat
54 3
2^1201046-1 361552 L77 2004
55 5025412^1199930-1 361221 L93 2004
56 292550^65536+1 358233 GC2 2002 Generalized Fermat
57 291726^65536+1 358153 GC2 2002 Generalized Fermat
58 71009
2^1185112-1 356760 L47 2004
59 255694^65536+1 354401 g266 2002 Generalized Fermat
60 691092^1157446+1 348431 SB4 2002
61 152713
2^1154707-1 347607 g23 2004
62 189590^65536+1 345887 g262 2002 Generalized Fermat
63 3501072^1144101-1 344415 L35 2004
64 209826493
2^1140855-1 343440 L10 2004
65 5006212^1138518-1 342734 L73 2004
66 504613
2^1136459-1 342114 L84 2004
67 141146^65536+1 337489 g281 2002 Generalized Fermat
68 108368^65536+1 329968 g181 2001 Generalized Fermat
69 4127172^1084409-1 326446 L76 2004
70 150847
2^1076441-1 324047 L73 2004
71 2098264932^1071303-1 322503 L10 2004
72 9
2^1051026+1 316392 p156 2004 Generalized Fermat
73 1212^1039965-1 313063 L65 2004
74 13
2^1038896+1 312740 g267 2004
75 212^1022168+1 307705 g279 2004
76 48594^65536+1 307140 g141 2000 Generalized Fermat
77 65567
2^1013803+1 305190 SB2 2002
78 8692^1000725+1 301252 p114 2005
79 32883
2^1000004+1 301036 p86 2002
80 441312^995972+1 299823 SB3 2002
81 3
2^992700-1 298833 L59 2004
82 1212^990219-1 298088 L66 2004
83 23
2^977541+1 294271 g267 2004
84 252^966414+1 290922 g279 2004 Generalized Fermat
85 11
2^960901+1 289262 g277 2005
Divides Fermat F(960897)
86 2431636632^919087-1 276682 L10 2004
87 3
2^916773+1 275977 g245 2001
Divides GF(916771,3), GF(916772,10)
88 2167512^903792+1 272074 g346 2004
89 309817
2^901173-1 271286 L64 2004
90 195811212^893547-1 268992 p49 2004
91 11
2^886071+1 266735 g277 2005
Divides GF(886070,12)
92 1705912^866870-1 260960 L47 2004
93 93997
2^864401-1 260216 L49 2004
94 195811212^862127-1 259534 p49 2003
95 2^859433-1 258716 SG 1994 Mersenne 33
96 21
2^856865+1 257944 g279 2004
97 192^853546+1 256945 g381 2005
98 9
2^834810+1 251304 p148 2004 Generalized Fermat
99 92^828709-1 249468 L38 2005
100 17
2^824451+1 248186 g267 2004


#18


Largest prime number ever is found

[ul]
[li] 15:11 02 December 2003[/li][li] NewScientist.com news service[/li][li]Will Knight[/li][/ul]

A 26-year-old graduate student in the US has made mathematical history by discovering the largest known prime number.

                	                                The new number is 6,320,430 digits long. It took just over two years to find using a distributed network of more than 200,000 computers.

                	                                Michael Shafer a chemical engineering student at Michigan State University used his office computer to contribute spare processing power to the Great Internet Mersenne Prime Search (GIMPS). The project has more than 60,000 volunteers from all over the world taking part.

                	                                "I had just finished a meeting with my advisor when I saw the computer had found the new prime," Shafer says. "After a short victory dance, I called up my wife and friends involved with GIMPS to share the great news." 

                	                                Prime numbers are positive integers that can only be divided by themselves and one. Mersenne primes are an especially rare type of prime that take the form 2 p-1, where p is also a prime number. The new number can be represented as 220,996,011-1. It is only the 40th Mersenne prime to have ever been found.

Found this here


#19

I doubt anyone could say what the largest prime number is, even the largest mersienne prime is limitless.

The largest prime number ever is obsolete before you finish writing it down :wink: