5000

# New largest prime number discovered!

Amaze your friends with our top facts about the new largest known prime number

Here at Chalkdust we’re very excited by the latest discovery of the new largest prime number, which is the Mersenne prime $2^{74,207,281}-1$. So to celebrate this discovery by the Great Internet Mersenne Prime Search, we thought we’d publish the number.

### Fun facts first:

• All Mersenne primes are of the form $2^p – 1$, where $p$ is prime (the first four are 3, 7, 31, and 127).
• Mersenne primes are named after Marin Mersenne (whose face is in the banner at the top!).
• In binary, the number is ‘1’ repeated 74,207,280 times!
• This means it requires 8.85MB of disk space to store, or 7 floppy disks!
• Using the “million, billion, trillion” naming system, you could call this number 300 septillisensquadragintaquadringentiilliquattuorducentillion!

### The new prime

Sadly it’s 22 million digits long, so we can’t publish it in its entirety, but it begins:

3003764180846061820529860983591660500568758630303014848439416933455477232190679942968936553007726883204482148823994267278352907009048364322180153481996522413722876843102133862845736663615066675321227728593598640577802568756477958658321420511711096358442629365726503872407101479826313204371431291121983921887612885039587719203550171864386658099542863444605366067617179336837496247567825783617310448839341553870852508685372972…

and ends with:

860347811180188837898128568440669359271612444713805577302483892184777905493456249144515504366735435257646973008855321674803866037094498725552912123074801792765597096176486305356033886997788467889060830923906229428002877708466815350114276229212218369040454779639313670134014480149404704116966334745646885160717774014762912462113646879425801445107393100212927181629335931494239018213879217671164956287190498687010073391086436351.

Thankfully it ends in a 1 and not a 2. You would be forgiven if you prefer to write it $3.0037 \times 10^{22,338,617}$.

There are, of course, an infinite number of primes, which we can prove using Euclid’s theorem (as featured in the Elements from 300 BC). The announcement by the GIMPS, a project looking for Mersenne primes as evidence suggests that Mersenne numbers are more likely to be prime than a randomly picked integer, is for the largest found so far.

The conjoined semicircles in the banner at the top of the page were generated by Jason Davies’ prime number pattern generator. Have a play!

Matt is a PhD student at UCL, working in the fields of general relativity and cosmology.
ucl.ac.uk/~ucahawr    + More articles by Matthew

Adam is a postdoctoral researcher at Imperial College London, where he investigates weird, non-Newtonian fluids. If he’s not talking about the maths of chocolate fountains he is probably thinking about fonts, helping Professor Dirichlet answer your personal problems, and/or listening to BBC Radio 2.
@Pecnut     adamtownsend.com    + More articles by Adam

Matthew Scroggs is a PhD student at UCL working on finite and boundary element methods. His website, mscroggs.co.uk, is full of maths and now features a video of him completing a level of Pac-Man optimally.
@mscroggs      mscroggs.co.uk    + More articles by Matthew

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