# new prime number found

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skafather84
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28 Sep 2008, 1:06 am

Mathematicians in California could be in line for a \$100,000 prize (£54,000) for finding a new prime number which has 13 million digits.

Prime numbers can be divided only by themselves and one.

The prize was set up by the Electronic Frontier Foundation to promote co-operative computing on the Internet.

The team from the University of California at Los Angeles (UCLA) found the new number by linking 75 computers and harnessing their unused power.

This enabled them to perform the enormous number of calculations needed to find and verify a new prime.

Thousands of people around the world linked the powers of their personal computers in the search for a higher "Mersenne" prime number - named after 17th-Century French mathematician Marin Mersenne.

Mersenne primes are expressed as two to the power of P, minus one - with P being itself a prime number.

Edson Smith, the leader of the winning UCLA team, told the Associated Press news agency: "We're delighted. Now we're looking for the next one, despite the odds."

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now....a basic question: how does this improve anything? is this merely mathematical trivia to be finding primes or is there any kind of applicable significance to the find?

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FerrariMike_40
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28 Sep 2008, 1:16 am

Do you know what the number is? Is it a X^Y - 1 prime, like the previous highest prime was

skafather84
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28 Sep 2008, 1:21 am

FerrariMike_40 wrote:
Do you know what the number is? Is it a X^Y - 1 prime, like the previous highest prime was

the article says 2^prime number - 1.

a mersenne prime.

so....is there any significance to this other than the trivia aspect?

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ValMikeSmith
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28 Sep 2008, 2:47 am

Quote:
Do you know what the number is?

Well, there are only 3 numbers with 13 million digits
that are also all ones in binary
like the mersenne primes always are.

richie
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28 Sep 2008, 6:50 am

Quote:
# n Mn Digits in Mn Date of discovery Discoverer
1 2 3 1 5th century BC[6] Ancient Greek mathematicians
2 3 7 1 5th century BC[6] Ancient Greek mathematicians
3 5 31 2 3rd century BC[6] Ancient Greek mathematicians
4 7 127 3 3rd century BC[6] Ancient Greek mathematicians
5 13 8191 4 1456 anonymous [7]
6 17 131071 6 1588 Cataldi
7 19 524287 6 1588 Cataldi
8 31 2147483647 10 1772 Euler
9 61 2305843009213693951 19 1883 Pervushin
10 89 618970019…449562111 27 1911 Powers
11 107 162259276…010288127 33 1914 Powers[8]
12 127 170141183…884105727 39 1876 Lucas
13 521 686479766…115057151 157 January 30, 1952 Robinson
14 607 531137992…031728127 183 January 30, 1952 Robinson
15 1,279 104079321…168729087 386 June 25, 1952 Robinson
16 2,203 147597991…697771007 664 October 7, 1952 Robinson
17 2,281 446087557…132836351 687 October 9, 1952 Robinson
18 3,217 259117086…909315071 969 September 8, 1957 Riesel
19 4,253 190797007…350484991 1,281 November 3, 1961 Hurwitz
20 4,423 285542542…608580607 1,332 November 3, 1961 Hurwitz
21 9,689 478220278…225754111 2,917 May 11, 1963 Gillies
22 9,941 346088282…789463551 2,993 May 16, 1963 Gillies
23 11,213 281411201…696392191 3,376 June 2, 1963 Gillies
24 19,937 431542479…968041471 6,002 March 4, 1971 Tuckerman
25 21,701 448679166…511882751 6,533 October 30, 1978 Noll & Nickel
26 23,209 402874115…779264511 6,987 February 9, 1979 Noll
27 44,497 854509824…011228671 13,395 April 8, 1979 Nelson & Slowinski
28 86,243 536927995…433438207 25,962 September 25, 1982 Slowinski
29 110,503 521928313…465515007 33,265 January 28, 1988 Colquitt & Welsh
30 132,049 512740276…730061311 39,751 September 19, 1983[6] Slowinski
31 216,091 746093103…815528447 65,050 September 1, 1985[6] Slowinski
32 756,839 174135906…544677887 227,832 February 19, 1992 Slowinski & Gage on Harwell Lab Cray-2 [9]
33 859,433 129498125…500142591 258,716 January 4, 1994 [10] Slowinski & Gage
34 1,257,787 412245773…089366527 378,632 September 3, 1996 Slowinski & Gage [11]
35 1,398,269 814717564…451315711 420,921 November 13, 1996 GIMPS / Joel Armengaud [12]
36 2,976,221 623340076…729201151 895,932 August 24, 1997 GIMPS / Gordon Spence [13]
37 3,021,377 127411683…024694271 909,526 January 27, 1998 GIMPS / Roland Clarkson [14]
38 6,972,593 437075744…924193791 2,098,960 June 1, 1999 GIMPS / Nayan Hajratwala [15]
39 13,466,917 924947738…256259071 4,053,946 November 14, 2001 GIMPS / Michael Cameron [16]
40[*] 20,996,011 125976895…855682047 6,320,430 November 17, 2003 GIMPS / Michael Shafer [17]
41[*] 24,036,583 299410429…733969407 7,235,733 May 15, 2004 GIMPS / Josh Findley [18]
42[*] 25,964,951 122164630…577077247 7,816,230 February 18, 2005 GIMPS / Martin Nowak [19]
43[*] 30,402,457 315416475…652943871 9,152,052 December 15, 2005 GIMPS / Curtis Cooper & Steven Boone [20]
44[*] 32,582,657 124575026…053967871 9,808,358 September 4, 2006 GIMPS / Curtis Cooper & Steven Boone [21]
45[*] 37,156,667 202254406…308220927 11,185,272 September 6, 2008 GIMPS / Hans-Michael Elvenich[2]
46[*] 43,112,609 316470269…697152511 12,978,189 August 23, 2008 GIMPS / Edson Smith[2]

* It is not known whether any undiscovered Mersenne primes exist between the 39th (M13,466,917) and the 46th (M43,112,609) on this chart; the ranking is therefore provisional. For a historical example, note that the 29th Mersenne prime was discovered after the 30th and the 31st. It is also remarkable that the current record holder was followed 14 days later by a smaller Mersenne prime.

To help visualize the size of the 46th known Mersenne prime, it would require 3,461 pages to display the number in base 10 with 75 digits per line and 50 lines per page.

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LostInEmulation
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28 Sep 2008, 6:58 pm

Primes do have certain applications in various fields, especially in public key cryptography. So... it's not only a game for mathematicians.

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lau
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28 Sep 2008, 7:25 pm

skafather84 wrote:
...

so....is there any significance to this other than the trivia aspect?

Almost every part of mathematics has started life as "trivia".

Indeed, I always have said that mathematics is entirely made of trivia. That's the way we mathematicians like it.

What happens, though, is the irritating "practical" people keep finding applications for every "trivial" new field of study we open up.

As to whether there is any particular importance to be attached to a 13 million digit Mersenne prime - time will tell. Maths has a habit of surprising people.

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YowlingCat
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28 Sep 2008, 7:29 pm

I run this on my desktop:

http://www.mersenne.org/freesoft.htm

richie
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28 Sep 2008, 8:17 pm

lau wrote:
skafather84 wrote:
...

so....is there any significance to this other than the trivia aspect?

Almost every part of mathematics has started life as "trivia".

Indeed, I always have said that mathematics is entirely made of trivia. That's the way we mathematicians like it.

What happens, though, is the irritating "practical" people keep finding applications for every "trivial" new field of study we open up.

As to whether there is any particular importance to be attached to a 13 million digit Mersenne prime - time will tell. Maths has a habit of surprising people.

Searching for and testing gigantic numbers does serve a practical purpose, and that is testing and developing faster algorithms and
processors for computers...computers that are used in medical and other research. Right now my computer is in the process of factoring the
467th Fibonacci number which has 98 digits...Here is the current state of its progress:

Quote:
17690617586682990180447203622188161240682337031027142006892310369574875779255058929007841461590953

First run:
17 690617 586682 990180 447203 622188 161240 682337 031027 142006 892310 369574 875779 255058 929007 841461 590953 is composite

After 5 hours:
Factoring 17 690617 586682 990180 447203 622188 161240 682337 031027 142006 892310 369574 875779 255058 929007 841461 590953
(98 digits)
Limit (B1=1000000; B2=100000000) Curve 779
Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
Probability: 100% 100% 100% 94% 23% 3%

And still chugging along.....

After 6 Hours:
Factoring 17 690617 586682 990180 447203 622188 161240 682337 031027 142006 892310 369574 875779 255058 929007 841461 590953
(98 digits)
Limit (B1=1000000; B2=100000000) Curve 879
Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
Probability: 100% 100% 100% 96% 28% 4%

And still chugging away....

http://www.alpertron.com.ar/ECM.HTM

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khelben1979
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02 Oct 2008, 8:13 am

Perhaps you people already know about PrimeGrid. But here it is: PrimeGrid homepage

I'm a member myself but if someone asked me what it does I wouldn't be able to answer, I think.