Turing and the Primes (2016) [pdf](people.maths.bris.ac.uk)
people.maths.bris.ac.uk
Turing and the Primes (2016) [pdf]
https://people.maths.bris.ac.uk/~maarb/papers/turingprimes.pdf
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Talking about primes,(2^136279841)-1 is the New Largest Known Prime Number. Discovered 21st Oct (Today).
Ref. https://www.mersenne.org/
Ref. https://www.mersenne.org/
Interestingly, the first more challenging program I wrote as a child was a prime counting program. Although I wanted a Jupiter Ace because I wanted to learn Forth, instead I had a Sinclair ZX80 with 8K ROM (and later a T/S 1000). With the speed of Sinclair BASIC, it'd've taken multiple years to count the first million primes, something that I use as a benchmark these days and which takes less than a second on an Apple ARM CPU.
I remember collecting counts to compare ln(x) with pi(x) and imagining how wonderful it'd be to have powerful computers that could give me the answers I wanted in seconds and minutes instead of days, weeks, months or years. I like to imagine Turing had imagined the same thing now and then :)