# Tag Archives: prime numbers

September 17, 2008, 11:56 am

# It's official: They're prime

The numbers believed to be the 45th and 46th Mersenne primes have been proven to be prime. The 45th Mersenne prime is $$2^{37156667} -1$$ and the 46th is $$2^{43112609} – 1$$.Full text of these numbers is here and here.

Of course what you are really wanting to know is how my spreadsheet models worked out for predicting the number of digits in these primes. First, the data:

• Number of digits actually in $$M_{45}$$: 11,185,272
• Number of digits actually in $$M_{46}$$: 12,978,189

My exponential model ($$d = 0.5867 e^{0.3897 n}$$) was, unsurprisingly, way off — predicting a digit count of over 24.2 million for $$M_{45}$$ and over 35.8 million for $$M_{46}$$. But the sixth-degree polynomial — printed on the scatterplot at the post linked to above — was… well, see for yourself:

• Number of digits predicted by 6th-degree polynomial model for $$M_{45}$$:…

October 17, 2007, 11:03 am