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PROOF 13

Prove.

1 is not prime

On the naturals ℕ.

What you may use

A11 ≤ a
1 is the least natural number
A2a × 1 = a
multiplicative identity
A3(ab)c = a(bc)
associativity of multiplication
A4b ≤ c ⟺ ab ≤ ac
multiplication and order
A5prime factorization is unique
fundamental theorem of arithmetic
Ea = b ⟹ apply the same operation to both sides
properties of equality

Nothing outside this list may be cited.

Definition D1

b | a means that a natural number k exists satisfying a = bk.

Proof.

Related labs

Prime Numbers lab →

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