Lehmer sieve

Derrick Norman Lehmer and his son Derrick Henry built a machine in 1926 to find numbers satisfying a set of congruences simultaneously — the core operation both in factoring and in proving a large number prime. Each chain was cut to a length matching one modulus, with holes drilled at the positions where the residue class fit. A lamp shone through the assembly onto a photocell behind it, and the instant every hole lined up the light got through and the motor stopped. The chains were bicycle chains for the unglamorous reason that they were cheap and available off the shelf.

The 1932 version swapped chains for gears and reached roughly 5,000 numbers per second — faster than any general-purpose machine would manage for decades, precisely because it could do exactly one thing. The younger Lehmer came back to the problem in 1946 and ran number theory on ENIAC over a weekend while the ballistics people were off duty. The lesson gets relearned at regular intervals: once the search space is large enough, purpose-built hardware beats the general case every time. FPGAs and ASICs are the same bargain in different materials.