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Just looking for the number asked in the question. I have a reason for wanting to know.

I've googled this question and the closest I have come to an answer is this:

"The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million or so (Ref Wiki)."

PAL
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I don't know whether this is a record, but it appears that http://compoasso.free.fr/primelistweb/page/prime/eratosthene_en.php used Eratosthenes to find all the primes up to $100,000,000,000$.

Gerry Myerson
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    Thanks Gerry. That's a far cry from 10,000,000. And that's basically all I wanted to know. – PAL Apr 13 '20 at 04:23