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.


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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