A new prime number has been discovered through a crowdsourced system – but it’s not from the Great Internet Mersenne Prime Project, about which I have written often. This was found by Seventeen or Bust, a similar project to find Sierpinski numbers.

I had never herd of Sierpinski although I, like you I suspect, know of the fractal shape called the Sierpinski triangle, produced by the same Polish mathematician) and they’re tricky: A Sierpinski number must be a positive, odd number, and takes the place of k in the formula k x 2^{n} + 1, for which all integers are composite, not prime. The new prime – 9 million or so digits long – was found as part of attempts to find the smallest possible Sierpinski number, reports Science Alert:

Over the past 50 years, mathematicians have found six possible candidates that could be the smallest possible Sierpinski numbers: 10,223, 21,181, 22,699, 24,737, 55,459 and 67,607. But so far, no one’s been able to prove that any of them are definitely a Sierpinski number. “To be certain you’re really dealing with a Sierpinski number requires a mathematical proof that no matter what choice of n you make, k × 2

^{n}+ 1 will never end up prime.” To know that, you have to know what numbers are prime numbers, and that’s where the PrimeGrid ‘Seventeen or Bust’ project comes in.

Mersenne primes are prime number of the form 2^{n} – 1. So far, 49 of them have been confirmed – the biggest having more than 22 million digits. I won’t write it down.