Light matrices of prime determinant by D. Goldstein, A. Hales, and R. Stong Our interest is in "light" square integer matrices with of prime determinant. The weight of a matrix is, by definition, the sum of the absolute value of its entries. For $p$ a prime, let $d(p)$ be the weight of the lightest integer matrix of determinant $p$. The quantity $d(p)$ may be difficult to compute exactly for large $p$. However it can be closely estimated. Our main result asserts that the limiting value of the quantity $d(p)/\log_2(p)$ is $2.5$, as $p$ tends to inifinity through prime values. A consequence of our analysis is that the primes that are determinants of the lightest possible matrices, in the sense that $d(p)/\log_2(p)< 2.5$, are precisely $p=2,7,13,37$ and those of the form $2^2^k+1$ (the Fermat primes).