I've been crunching large numbers that involve 2 for a long time. They're mainly primality tests for k*

**2**^n-1, k*

**2**^n+1, and

**2**^p-1.

So I thought, why not calculate something else that also involves 2? But instead of crunching such huge numbers, why not work on something much smaller that has the bulk of its digits on the other side of the decimal point?

Well, here it is. I calculated the natural logarithm of 2 (which is 0.69314718...) to 6x10^11 decimal digits, setting a new world record!

http://www.numberworld.org/y-cruncher/
Surprisingly, running this calculation didn't cause much of a conflict with prime hunting. That's because the bottleneck for calculating constants to billions of decimal places is not CPU speed (like it is for prime hunting), but hard disk input/output. As a side note, the program I used to calculate ln (2) is also the same program used to calculate pi to a record 22,459,157,718,361 decimal digits:

https://fivethirtyeight.com/features...the-end-of-pi/
The motivation for calculating constants and for finding large primes is remarkably similar. They're both used for bragging rights and for testing hardware, but the deeper appeal is to satisfy human curiosity and the opportunity to add to the sum total of human knowledge without needing special talents, a college degree, or a large personal time commitment. We know that pi=3.14159...9237..., but what comes after that 7? Similarly, what is the next Mersenne prime after M51? And how is their distribution? Are Mersenne primes clustered together, and is ln (2) a normal number?

We may never know the answers, but the journey is just as fun as the destination.