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    If such a number exists, then P is incomplete and therefo... — Carmelics
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    Supports→The set of prime numbers is infinite.

    If such a number exists, then P is incomplete and therefore not a complete list of all primes.

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    Multiplying all elements of P and adding 1 yields a number that cannot be divide...Suppose the set of primes P is finite.The set of prime numbers is infinite.This contradiction shows the assumption that P is finite must be false.

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    Suppose the set of primes P is finite.78%The sentence 'There are infinitely many prime numbers' can be literall...77%F ⊢ Prf_F(n̲, ⌈G_F⌉) would contradict Gödel's incompleteness theorem77%If P ⊊ NP, then NP-complete problems are not in P.77%

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    (Ir)regularity of the set of primes. Since antiquity it is known that there is an infinite number of primes. The proof is simple. Suppose the set of primes P is finite. Now multiply all elements of P and add 1. The resulting number cannot be divided by any member of P, so P is incomplete. An estimation of the density of the prime numbers given by the Prime Number Theorem (see entry in Encyclopaedia Britannica on Prime Number Theorem [OIR]). It states that the gaps between primes in the set of

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