Looking at how a list of primes is computed with the help of digital computing machinery during the years 1929 to 1949 gives an interesting insight into the complex interrelations between the mathematics of the problem, the pecularities of the machine and the logical planning of the computation. It also allows for close-reading through this specific example some aspects of the crucial birth period of the modern digital computers, aspects related both to the hardware and the "software".
The idea to use machinery for computing primes originated with the mathematician D.H. Lehmer who devised several special purpose machines. The idea is later taken up by C. E. Shannon as an example in his master's thesis on circuitry. Finally, the prime computations reappear, alongside list of squares and cubes, as exemplary computations on the ENIAC and on the EDSAC. The historical sequence of computing prime numbers is marked by a turn from dedicated hardware to writing and debugging software.