Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html

Problem 7 of the Hundred-dollar, Hundred-digit Challenge Problems,
SIAM News, vol 35, no. 1.

7. Let A be the 20,000 x 20,000 matrix whose entries are zero
everywhere except for the primes 2, 3, 5, 7, . . . , 224737 along the
main diagonal and the number 1 in all the positions A(i,j) with
|i-j| = 1,2,4,8, . . . ,16384.  What is the (1,1) entry of inv(A)?

http://www.siam.org/news/news.php?id=388