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13-million-digit prime number


Hanoi5

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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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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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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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From Wikipedia:
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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From Wikipedia:
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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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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