Reply to post: So "known" primes could be invalidated?

Give a boffin a Xeon and a big GPU, get a new big prime number

2Nick3

So "known" primes could be invalidated?

This is all well past the math I studied, but if this is the 12th largest prime number, isn't there the possibility that we could find two new "lower ranked" primes that are the prime factors to a "higher ranked" prime?

Say we "know" Prime2 is a prime, but discover Prime12 and Prime7, and they are the two prime factors of Prime2, so that Prime12 x Prime7 = Prime2. We just invalidated Prime2 as a prime number.

We know 11 is a Prime number because we know all of the prime numbers below it. If we assume 221 is a prime but don't know 13 and 17 are primes we are wrong because of incomplete information. If we subsequently discover that 13 is a prime number, we then invalidate 221 as a prime.

Or is there a better proof that someone has come up with?

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