In this paper the problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed. Because the result inverse function is given as a Fourier cosine series, the procedure requires only about ten FORTRAN statements. Furthermore, it does not require the use of involved algorithms for the generation of any special functions, but uses only cosines and exponentials. The basis of the method hinges on the fact that in evaluating the inverse Laplace transform integral there exists a freedom in choosing the contour of integration. Given certain restrictions, the contour may be any vertical line in the right-half plane. Specifying a line, the integral to be evaluated is essentially a Fourier integral. However, the method is concerned with determining the proper line, so that when the integral (along this line) is approximated, the error is as small as desired by virtue of having chosen the particular contour.

Abstract. Extending previous searches for prime Fibonacci and Lucas num-

In this paper the use of the techniques of queueing theory in analyzing the perform~nce of a mass storage device in a reM-time environment is demonstrated; concern is with the tradeoff experienced in practice between throughput of a stochastic service device and the response time for each service request. For concreteness, the analysis is applied to the IBM 2314 disk storage facility. The results are presented irL a series of graphs showing the file system response time versus the throughput for several distributions of record length and arm movement. The queueing model and the theoretical tools used are described in sufficient detail to permit the reader to apply the techniques to other systems. In particular, any disk whose seek time characteristic can be approximated by a pieeewise linear continuous function may be analyzed by the methods presented.KEY WORDS AND PHRASES: reM-time systems, time-sharing systems, disk storage, IBM 2314, file system performance, queueing analysis, Pollaczek-Khintchine formula, M/G/1 queue in tandem, response time distribution, numerical inversion of Laplace transforms ca CATEGORIES: 3.72, 3.80, 5.50, 6.34

Abstract.Generalized repunits have the form (bn -l)/(è -1). A table of generalized repunit primes and probable primes is presented for b up to 99 and large values of n .

Abstract. Numbers of the form F b,n = b 2 n +1 are called Generalized Fermat Numbers (GFN). A computational method for testing the probable primality of a GFN is described which is as fast as testing a number of the form 2 m −1. The theoretical distributions of GFN primes, for fixed n, are derived and compared to the actual distributions. The predictions are surprisingly accurate and can be used to support Bateman and Horn's quantitative form of "Hypothesis H" of Schinzel and Sierpiński. A list of the current largest known GFN primes is included.