this post was submitted on 22 Jan 2024
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How many primes are there before 1 and 2^31. IIRC prime numbers get more and more rare as the number increases. I wouldn't be surprised if this would pass 99% of tests if tested with all positive 32 bit integers.
Per the prime number theorem, for large enough N the proportion of primes less than or equal to N is approximately 1/log(N). For N = 2^(31) that's ~0.0465. To get under 1% you'd need N ~ 2^(145).
So you better use 128-bit unsigned integers 😅
Wolfram alpha says it's about 4.9%. So 4.9% of numbers in the range 1 to 2^31 are prime. It's more than I expected.