User blog comment:SuperJedi224/A Programming Challenge/@comment-5529393-20150325003513

Here's an entry:

[pre] >>>+++++[<<<+[>>+<<-]>>[<<+[>++<-]>[<+>-]>-]>-] [/pre]

47 characters.

[>++<-] reduces the current cell by n and increases the next cell by 2n [<+>-] reduces the current cell by n and increases the previous cell by n so +[>++<-]>[<+>-] changes the first cell from n to 2n+2 [<<+[>++<-]>[<+>-]>-] decrements the third cell one at a time and performs the previous operation until the third cell reaches zero, so if the third cell has n, the first cell becomes 2^(n+1)-2. +[>>+<<-] reduces the first cell by n and increases the third cell by n+1 [<<<+[>>+<<-]>>[<<+[>++<-]>[<+>-]>-]>-] performs the previous operations and decrements the fourth cell until the fourth cell becomes zero.

The program increments the fourth cell to 5 and then performs the above loop 5 times, applying the function 2^(n+2)-2 five times to the first cell. It becomes 2, 14, 2^16-2, 2^2^16-2, and finally 2^2^2^16-2, which is indeed bigger than 10^10^10.

The program can naturally be extended to more cells, getting one more Knuth arrow each time.