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what is the Best known Upper bound on Twin Primes?

Do we know for sure that there aren't any prime numbers smaller than the current biggest known prime?

  • Do we even know if it is probable or not? Here's another one... Based on the gaps between all the known primes to date (taking into account possibilities of undiscovered primes that're smaller than other known primes) what is the next biggest prime to be discovered most likely to be?... approximately... Is there a number which the next biggest prime to be discovered has a 50:50 probability of being bigger/smaller than?

  • Answer:

    There probably are undiscovered primes smaller than the largest known one. Computers searching for large primes usually only check the primality of Mersenne numbers (of the form 2^n-1), because they are easier for the binary programme to manage and have an unusually high density of primes.

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There probably are undiscovered primes smaller than the largest known one. Computers searching for large primes usually only check the primality of Mersenne numbers (of the form 2^n-1), because they are easier for the binary programme to manage and have an unusually high density of primes.

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You need to look up the 'understated prime conjecture' (which becomes the overstated prime conjecture for very large primes ) This give you an idea as to the relative density of primes and thus the probability of how far to go to find a prime from a given prime. I think it was Gauss who formulated it. Also look for Skewes Number!

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You need to look up the 'understated prime conjecture' (which becomes the overstated prime conjecture for very large primes ) This give you an idea as to the relative density of primes and thus the probability of how far to go to find a prime from a given prime. I think it was Gauss who formulated it. Also look for Skewes Number!

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