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New to this, sorry for bad formatting but:

The largest know prime number is a Mersenne Prime Number, i.e. it is in the form $2^n-1$. Whilst this is big, the last known prime number before this was millions of digits shorter. Take the list $2, 3, 5, 7, 11,\cdots$ in the list $11$ is the largest (prime) number. We know all the prime numbers before $11$, though. So, a better way to ask would be as stated below:

What is the largest prime number where we know all the prime numbers before it? Doing some research, I've found that we know the first $50$ million primes or so, but I'm sure with all the computing power we humans have, that cannot be the limit.

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marked as duplicate by Henning Makholm, Robert Soupe, Community Dec 23 '16 at 22:31

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  • $\begingroup$ Say what? $ $ $ $ $\endgroup$ – Kaster Dec 23 '16 at 21:45
  • $\begingroup$ Sometimes I think it pays to just use some part of the question as the title; in this case that would be, "What is the largest prime number where we know all the prime numbers before it?" That seems a perfectly clear statement of the question and I can't think of a better way to ask it in so many words. $\endgroup$ – David K Dec 23 '16 at 21:54
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    $\begingroup$ My guess is that it's much greater than $10^{100}$. Wolfram Alpha takes barely a couple of seconds to tell me that $10^{100} + 267$ is the next prime. My next query gave me the prime $10^{1000} + 453$. $\endgroup$ – Robert Soupe Dec 23 '16 at 22:01
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    $\begingroup$ @RobertSoupe: That would require a somewhat flexible definition of "known". All of the primes below $10^{100}$ cannot possibly be listed explicitly anywhere -- the observable universe contains too little matter to build enough storage media for that. $\endgroup$ – Henning Makholm Dec 23 '16 at 22:08
  • $\begingroup$ How many prime numbers are known? is a near-duplicate of this. $\endgroup$ – Henning Makholm Dec 23 '16 at 22:09

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