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.
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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:

"Huge new prime number discovered"

BBC, 5 December 2001,"The largest prime number yet discovered has just been revealed to the world. The new number, expressed as 2^13,466,917-1, contains 4,053,946 digits [and] was discovered by Michael Cameron, a 20-year-old Canadian..."

Metro, 4 December 2003, "The maths world was celebrating last night after the discovery of the largest known prime number. It has 6,320,430 digits ... American Michael Shafer found it after joining the Great Internet Mersenne Prime Search. He said: 'After a short victory dance, I rang my wife and GIMPS friends'".

Metro, 5 January 2006, "After years of calculating [a computer] has come up with a prime number 9.1 million digits long - the largest ever found. Steve Boone, who led the study at Central Missouri State University, said: 'We are very excited.'"

BBC, 28 September 2008, "Mathematicians in California could be in line for a $100,000 prize (£54,000) for finding a new prime number which has 13 million digits. Edson Smith, the leader of the winning UCLA team, told the Associated Press news agency: 'We're delighted. Now we're looking for the next one, despite the odds.'"

If there is a pattern here, and in maths there usually is, it takes an average of 830 days to discover a new prime number, and the number of digits goes up by 48% each time, so the next prime number will have about 19 million digits and will be discovered on 5 January 2011.