# Prime numbers

## Primal scream

243112609-1 is the world’s largest known prime number. Written down in full it’s 12,978,189 digits long. That would take a long time to read out, let alone scream. It would be much simpler to type it out. Maybe.

Reproduced in real life this number would stretch for up to 32km. Depending on the typeface. Different fonts apparently produce markedly different results.

Prime numbers are also, apparently, useful for things other than cryptography.

In case you’re wondering, prime numbers aren’t just the stuff of academic longhairs: like typefaces, they have interesting properties that make them strangely useful. The classical example comes from mechanical engineering, where two meshed gears will wear most evenly if each has a coprime number of teeth, since this evenly distributes the possible ways in which they interact (thereby minimizing the effects of any irregularities.) Some have suggested that 13- and 17-year cicadas each follow prime numbered life cycles in order to ensure that their populations compete as little as possible, coexisting only once every 221 years.

I know this, and now so do you, because of here, and here.

## Optimum prime

From the SMH…

“Mathematicians at the University of California, Los Angeles have discovered a 13 million-digit prime number, a long-sought milestone that makes them eligible for a \$US100,000 prize.

The group found the 46th known Mersenne prime last month on a network of 75 computers running Windows XP. The number was verified by a different computer system running a different algorithm.”

This number would be a 13mb .txt file on your computer.

From the ABC:

“Most people in Queensland don’t know what a prime number is”

…after SEVEN straight callers failed to answer the question in the afternoon quiz.

For those of you who forget:

“Primes are numbers like three, seven and 11 that are divisible by only two whole positive numbers: themselves and one.”

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