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I only just now understood that Euclid's method doesn't necessarily generate a prime number; it produces a number that you can't "get to" by multiplying the pri
by human20190310 7y ago
I only just now understood that Euclid's method doesn't necessarily generate a prime number; it produces a number that you can't "get to" by multiplying the primes in your list of prime numbers; as such any list of primes is incomplete.
- eridius 7y agoAnd since you can't "get to" it with your existing list, this means the prime factorization of this new number includes at least one prime not on your list, and therefore you can grow your list with every step (assuming you're capable of prime factorizing arbitrary numbers).