# The largest prime ever – you saw it here first

The GIMPS project says they've found the largest prime number ever, but they're keeping quiet about what it is until they've verified it (they expect to be done in a couple of weeks.)

Pshaw.  I can tell you right now what their prime number is.

Since I'm a computer scientist I'll write it down in binary.

GIMPS' LARGEST PRIME NUMBER IS (scroll down / highlight to view:)

0b
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
...
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111

EDIT: On Saturday 9/6 another prime was found.  They're also keeping mum about what this one is.  But I know this one too...

EDIT2: Every new Mersenne prime also means a new perfect number is discovered; counting these two new Mersenne primes, there are now 46 known perfect numbers, all of them even.  (It is conjectured, but not proven, that all perfect numbers are even.)  To go from a Mersenne prime (which is of the form 0b111...11, where there are a prime number of 1's) to its corresponding perfect number, tack on one fewer number of 0's onto the end of the number: e.g., 0b11 (3, the first Mersenne prime) becomes 0b110 (6, the first perfect number;) 0b111 (7, the second Mersenne prime) becomes 0b11100 (28, the second perfect number) etc. (The proof that such numbers are perfect is simple; there is a more complicated proof that all even perfect numbers are of this form.)

EDIT: I can now reveal that the number of 1s is 43,112,609.

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