These are a set of 24 Fortran DO-loops (The Livermore Fortran Kernels, LFK) extracted from operational codes used at the Lawrence Livermore National Laboratory . They have been used since the early seventies to assess the arithmetic performance of computers and their compilers. They are a mixture of vectorisable and non-vectorisable loops and test rather fully the computational capabilities of the hardware, and the skill of the software in compiling efficient code, and in vectorisation. The main value of the benchmark is the range of performance that it demonstrates, and in this respect it complements the limited range of loops tested in the LINPACK benchmark. The benchmark provides the individual performance of each loop, together with various averages (arithmetic, geometric, harmonic) and the quartiles of the distribution. However, it is difficult to give a clear meaning to these averages, and the value of the benchmark is more in the distribution itself. In particular, the maximum and minimum give the range of likely performance in full applications. The ratio of maximum to minimum performance has been called the instability or the speciality , and is a measure of how difficult it is to obtain good performance from the computer, and therefore how specialised it is. The minimum or worst performance obtained on these loops is of special value, because there is much truth in the saying that ``the best computer to choose is that with the best worst-performance''.