Two Very Large primes

As promised, I can now reveal the identity of the two newly discovered Mersenne primes. The smaller of the two, discovered on September 6 by Hans-Michael Elvenich in Langenfeld, Germany, is

2^{37,156,667} - 1,

an 11,185,272-digit number which you can download here. The larger one was actually discovered first, on August 23, by Edson Smith, who had installed the prime-checking software on computers at UCLA. It is now the largest known prime, weighing in at a whopping 12,978,189 digits, and is equal to

2^{43,112,609} - 1.

You can download it here. Of course, as I suspected, these are both longer than ten million digits, which means that the first one to be discovered is eligible for a $100,000 prize!

These are ridiculously huge numbers. For a little perspective, the total number of atoms in the universe is estimated at somewhere around 10^{80}, a number with only eighty-one digits. Now go back and read again how many digits these newly discovered prime numbers have.

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3 Responses to Two Very Large primes

  1. These discoveries may be useless to humanity, but they make a fair amount of money for the discoverers. Almost a penny per digit. Who exactly pays?

  2. Marty says:

    The EFF pays for the prize. Relax, it’s not taxpayer-funded.

  3. Brent says:

    If you read on this page you’ll see that the money comes from an individual donor.

    And I wouldn’t be so quick to say that they are useless to humanity. Certainly they are immediately useless to humanity. But basic research in distributed computing and computational number theory have already generated indirect benefits. Useful applications of technology and knowledge don’t come out of nowhere–they often start with basic research that, at the time, doesn’t look like it has much purpose.

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