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Largest prime numbers discovered are continuously updated, however it is not clear how many consecutive prime numbers have been discovered.

My question is : How many consecutive prime numbers have been discovered? In other words , what's the largest natural number N such that all primes ≤N are known.

Edit: It was suggested that am I asking what is the total number of prime numbers discovered? My answer is no. I am asking how many consecutive prime numbers have been discovered? For example - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103 and so on…

SacrificialEquation
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    Referring to "consecutive prime numbers" is confusing. I think you mean something like "what's the largest natural number $N$ such that all primes $≤N$ are known?" – lulu Jan 29 '24 at 16:21
  • @lulu Yes. I will put that in the question. – SacrificialEquation Jan 29 '24 at 16:27
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    As to the question, I would guess it is a moving target. New techniques and new programs are being run all the time. For whatever reason, this sort of list has not attracted the same attention as the search for the largest prime, so I'm not sure anyone is keeping track of the running streak of primes. – lulu Jan 29 '24 at 16:32

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Nobody calculates large number of primes and records them.

I could for a reasonable amount of money attach a few hundred terabytes of storage to my computer. Say 512 TB. That’s enough for 5 x 10^14 primes. It’s easier to calculate the primes when you need them. Primes up to 10^18 have been calculated and can be calculated again; that doesn’t count as “known”.

Twin primes wouldn’t be worth storing. Maybe quad primes, that’s sets of four primes 10k + 1, 3, 7 and 9. (They actually have the form 30k + 11, 13, 17 and 19).

gnasher729
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