Programming Primes (1968–1976): A Paradigmatic Program and Its Incarnations in the Age of Structured Programming

Abstract

International audienc

Computing Primes (1929-1949): Transformations in the Early Days of Digital Computing

“…It also showed that digital computing could not only tackle the practical problems in ballistics or other problems related to differential equations and continouous mathematics that analogue machines could handle already, but new classes of problems altogether. Lastly, the little number-theoretical programs contained enough logical complexity, using all or most elementary instructions, so that they were good 13 This posterity of the EDSAC primes program is framed in a broader historical context in [8].…”

“…Because the ENIAC card reader was slow (compared to its computation time, viz. 0.48 s versus .2 ms) and memory was at a premium, 8 Lehmer decided not to input the list of prime numbers via punched cards, but to let the ENIAC calculate its own primes, using Eratosthenes' sieve. To start with, Lehmer only sifted through the odd numbers, stepping +2 for each new number P .…”

“…Lehmer had also planned to use the (parallel, unconverted) ENIAC to calculate roots of the Riemann zeta-function [27, p. 293], but never got the chance once the ENIAC was rewired and intensively used by other groups involved in computational work of a more pressing, mostly military or 8 The ENIAC disposed of 20 words of memory that could change during computation (the 20 accumulators) and of 3 times 104 words of fixed memory that could not be changed during computation (the 3 function tables). This was hardly enough to hold all primes less than 1,000,000. industrial, nature.…”