Friday, 22 January 2016

Typical, you wait for ages...

… and ages and ages, and along comes another prime number.

The largest known prime number is now almost five million digits longer than the previous record-holder.

In a computer laboratory at a satellite campus of the University of Central Missouri, an otherwise nondescript desktop computer, machine No. 5 in Room 143, multiplied 74,207,281 twos together and subtracted 1. It then checked that this number was not divisible by any positive integer except 1 and itself — the definition of a prime number.

This immense number can only be practically written down in mathematical notation using exponents: 2^74,207,281 – 1. The previous largest was 2^57,885,161 – 1, which has a mere 17 million or so digits.

So, just to sum up the last few discovered primes:

Jan 2016: 22 million digits
Feb 2013: 17 million digits
Sept 2008: 13 million digits
Jan 2006: 9 million digits
Dec 2003: 6 million digits
Dec 2001: 4 million digits

For some reason, they are usually discovered in December or January. A coincidence? I think not.

What is almost certainly not a coincidence is that you get a surprisingly straight line when you plot the number of digits against the year it was discovered:


8a7d44b2-c230-11e4-a501-b78fe07746c6 said...

Frank Davis (banging on about the smoking ban) blogger and his team of experts regularly discover new evidence that shows on a graph a straight line from smoking kills to smoking never killed anyone.

Its number crunching magic.


The Stigler said...

Fascinating observation. Consistent fall in computing cost over time?

Prime number finders are pretty much - take a number, calculate the square root and count from 2 to the square root, dividing it, checking the result. It's nothing but a brute exercise. The time to do an extra digit should normally require a even more time than the last one, but when you factor in the falling cost of computing power, maybe that flattens it out.

Mark Wadsworth said...

R, FD is very good at that sort of thing, he's a proper mathematician/scientist.

TS, exactly. But each time you add a digit, you have ten times as many numbers to check, so on that basis, computers are getting ten times as fast at number crunching each year. Or something like that.