← MATH 01352 · Theory of Numbers
MATH 01352 · Divisibility & primes
Primes and infinitude proof idea
Definition
A prime has exactly two distinct positive divisors: 1 and itself. Euclid’s theorem: infinitely many primes — given p₁…pₖ, consider N=p₁…pₖ+1; a prime factor of N is new.
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Variants produce primes in certain forms; the basic proof is must-know.
Prime gaps can be arbitrarily large even though primes are infinite.
Twin prime conjecture etc. are open — good cultural math.
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Try this
Attempt each problem first, then open the worked solution.
1.Write Euclid’s infinitude proof in your own words (paragraph).