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2 hours ago comment added Dood Thank you for your detailed answer, Professor @WillSawin , Daniel Weber. I’ve added a follow-up to the original question to clarify and expand on my inquiry. I’d greatly appreciate it if you could take a look when you have a moment.
2 hours ago comment added Daniel Weber It might be better to sieve around $n$ using small-ish primes (like in the segmented sieve algorithm) before doing expensive primality tests
2 hours ago history answered Will Sawin CC BY-SA 4.0