Coding classes in Cambridgeshire

Method one is trial division: test each number by dividing it by the primes found so far, stopping at its square root. It remembers only the primes themselves. Method two is the sieve of Eratosthenes: write down every number, then cross out the multiples of each prime in turn; whatever survives is prime. It does far less work but needs a mark for every number. The learner codes both, checks that they produce exactly the same list, and counts the steps. To make the cost concrete we price each counted step as one EDSAC instruction at 650 a second, a deliberate simplification, since a real division took EDSAC far longer than an addition.

Read the last column against the last row. The plain sieve is the fastest, but ten thousand marks will never fit in 512 words. Trial division is frugal, but even the list of primes it must keep, 1,229 of them, is more than twice EDSAC's early memory. The segmented sieve gets both wins at once: it sieves 256 numbers at a time, keeping only those 256 marks plus the 25 small primes below 100 that it needs to do the crossing out, 281 words in all. It does exactly the same 16,979 crossings-out as the full sieve, because it is the same work done in slices.

Push the target to a hundred thousand and the gap widens: trial division needs 744,435 divisions, about 19 minutes at our rate, while the sieve needs 193,076 crossings-out, about five minutes, and the segmented version still fits in 321 words. The general lesson reaches far beyond primes. Speed and memory can often be traded against each other, and sometimes a smarter structure gives you both. Recognising which situation you are in is a large part of what it means to design software.

So a Cambridgeshire teenager should learn to program in 2026 for the same reason EDSAC's users did: to make a limited machine do useful work, and to know which limit matters. The longer argument is in why teenagers should still learn to code in 2026.