From 8b996d27105082e22c3dd5ec39334495bea78775 Mon Sep 17 00:00:00 2001 From: Tyler Perkins Date: Tue, 2 Nov 2021 16:00:01 -0400 Subject: [PATCH] Update for 02-11-21 16:00 --- index.wiki | 2 ++ math/index.wiki | 4 ++++ math/prime.wiki | 23 +++++++++++++++++++++++ 3 files changed, 29 insertions(+) create mode 100644 math/prime.wiki diff --git a/index.wiki b/index.wiki index 4f6c617..9d4a56f 100644 --- a/index.wiki +++ b/index.wiki @@ -51,6 +51,8 @@ _Ideas.md and Classes.md are encrypted, so these links will not work_ == [[math/index|Math]] == +See [[math/index|Math]] + == [[botany/index|Botany]] == * [[botany/vegies|Vegies]] diff --git a/math/index.wiki b/math/index.wiki index b36af7f..e550303 100644 --- a/math/index.wiki +++ b/math/index.wiki @@ -5,3 +5,7 @@ The purest study of them all == Topics == * [[proofs]] + +=== Number Theory === + +* [[prime]] diff --git a/math/prime.wiki b/math/prime.wiki new file mode 100644 index 0000000..c49697a --- /dev/null +++ b/math/prime.wiki @@ -0,0 +1,23 @@ += Primes = + +A Prime is a natural number that is only divisible by one and itself. + +== Prime factorization == + +Everynumber is either a Prime or a product of several primes together. This is +called prime factorization. + +== Euclid's Proof == + +Euclid Prooved that that are infinitely many primes in existance. The proof is +as follows + +1) Let p,,1,, , p,,2,, , p,,3,, , etc be an infinite list of primes +2) Let P be the product of all of those primes, and q be P + 1 +3) If q is a prime then there is at least one more prime that is not in the + list, namely, q +4) If q is not prime, then some prime factor p divides into q. If this factor p + were in the list, then it would divide P; However p also divided P+1=q. If p + divides P and also q, then p must also divide the difference of the two + numbers, which is (P+1)-P, or 1. Since no prime divides 1, p cannot be on + the list. This means at least one more prime exists beyond those in the list