## 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: