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13-million-digit prime number Just amazing...

#1 User is offline   Hanoi5 

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Posted 2008-September-27, 18:13

http://www.latimes.com/news/nationworld/na...story?track=rss

How many digits will the next one have?

 wyman, on 2012-May-04, 09:48, said:

Also, he rates to not have a heart void when he leads the ♥3.


 rbforster, on 2012-May-20, 21:04, said:

Besides playing for fun, most people also like to play bridge to win


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#2 User is offline   OleBerg 

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Posted 2008-September-28, 02:40

Hanoi5, on Sep 28 2008, 02:13 AM, said:

http://www.latimes.com/news/nationworld/na...story?track=rss

How many digits will the next one have?

More.
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#3 User is offline   EricK 

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Posted 2008-September-28, 04:09

OleBerg, on Sep 28 2008, 08:40 AM, said:

Hanoi5, on Sep 28 2008, 02:13 AM, said:

http://www.latimes.com/news/nationworld/na...story?track=rss

How many digits will the next one have?

More.

See

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

The one mentioned in the OP was the one discovered on August 23. The next one they found (on September 6) had fewer digits!
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#4 User is offline   gwnn 

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Posted 2008-September-28, 04:31

Yep it's amazing how many people look for prime numbers when there's evil threats like global warming, cancer, famine and global unhappiness in general abound. Luckily we have dedicated individuals like shubi who look for solutions for these issues.
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#5 User is offline   Al_U_Card 

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Posted 2008-September-28, 05:57

Personally, I prefer prime rib... :)
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#6 User is offline   pigpenz 

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Posted 2008-September-28, 06:58

EricK, on Sep 28 2008, 05:09 AM, said:

OleBerg, on Sep 28 2008, 08:40 AM, said:

Hanoi5, on Sep 28 2008, 02:13 AM, said:

http://www.latimes.com/news/nationworld/na...story?track=rss

How many digits will the next one have?

More.

See

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

The one mentioned in the OP was the one discovered on August 23. The next one they found (on September 6) had fewer digits!

saw where the forumula for a Mersene prime was 2p-1
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#7 User is offline   kenberg 

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Posted 2008-September-28, 07:50

Just out of curiosity, does anyone know the larges non-Mersenne prime that has been found? I suppose NSA regards this as a state secret since I assume the codes use non-Mersenne primes. Using a published list of primes would not seem very clever. Obviously I know approximately zip about all of this.
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#8 User is offline   EricK 

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Posted 2008-September-28, 10:17

kenberg, on Sep 28 2008, 01:50 PM, said:

Just out of curiosity, does anyone know the larges non-Mersenne prime that has been found? I suppose NSA regards this as a state secret since I assume the codes use non-Mersenne primes. Using a published list of primes would not seem very clever. Obviously I know approximately zip about all of this.

The numbers used in cryptography are many orders of magnitude smaller than these giants.

The primes are find by picking large numbers of the size you want and running "primality tests" on them until you find a prime. Note that primality testing is much faster than factorization (at least wih current methods!)

Please note however that I only know slightly more than zip about this.
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#9 User is offline   brianshark 

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Posted 2008-September-29, 04:06

From Wikipedia:

Quote

The largest known prime that is not a Mersenne prime is 19,249 × 2^13,018,586 + 1 (3,918,990 digits), a Proth number. This is also the seventh largest known prime of any form. It was found on March 26, 2007 by the Seventeen or Bust project and it brings them one step closer to solving the Sierpiński problem.
Edited to correct missing ^ in the number.
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#10 User is offline   EricK 

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Posted 2008-September-29, 16:58

brianshark, on Sep 29 2008, 10:06 AM, said:

From Wikipedia:

Quote

The largest known prime that is not a Mersenne prime is 19,249 × 213,018,586 + 1 (3,918,990 digits), a Proth number. This is also the seventh largest known prime of any form. It was found on March 26, 2007 by the Seventeen or Bust project and it brings them one step closer to solving the Sierpiński problem.

Just to clarify, that should read 19,249 × 2^13,018,586 + 1
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#11 User is offline   Lanor Fow 

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Posted 2008-September-30, 05:33

Primes in cryptography are normally in the region of 128 to 1024 long (or that order of magnitude).

Even if all of these were published it wouldn't make a difference to the strength of cyphers (well nto a significant difference) as the number of primes 1024 digits long is immense, testing them all is not a significantly easier problem than factorising the 2048 digit number in the first place.
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#12 User is offline   Gerardo 

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Posted 2008-October-02, 00:40

that's in bits, that is, in the 2^128-2^1024 range
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