24 lines
950 B
Plaintext
24 lines
950 B
Plaintext
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= Primes =
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A Prime is a natural number that is only divisible by one and itself.
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== Prime factorization ==
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Everynumber is either a Prime or a product of several primes together. This is
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called prime factorization.
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== Euclid's Proof ==
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Euclid Prooved that that are infinitely many primes in existance. The proof is
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as follows
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1) Let p,,1,, , p,,2,, , p,,3,, , etc be an infinite list of primes
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2) Let P be the product of all of those primes, and q be P + 1
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3) If q is a prime then there is at least one more prime that is not in the
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list, namely, q
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4) If q is not prime, then some prime factor p divides into q. If this factor p
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were in the list, then it would divide P; However p also divided P+1=q. If p
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divides P and also q, then p must also divide the difference of the two
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numbers, which is (P+1)-P, or 1. Since no prime divides 1, p cannot be on
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the list. This means at least one more prime exists beyond those in the list
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