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On Wed, 6 Sep 2017, Isaac M. Bavaresco wrote:
> Dear All,
> Today I woke up with a silly idea about prime numbers in my head:
> What is the proof that there are infinitely many prime numbers? One of
> such proofs was in my mind.
> Then I Googled and found Euclid's Proof. It is much similar to mine but
> not exactly the same.
> My proof:
> Consider a finite list of consecutive prime numbers starting in 3: 3, 5,
> 7, 11, ..., Pn.
> Let P be the product of all the prime numbers in the list.
> Let Q = P + 2. Let's prove that Q is prime:
> P + 1 is even (not prime)
> P + 3 is multiple of 3 (not prime)
> P + 5 is multiple of 5 (not prime)
> P + Pn is multiple of Pn (not prime)
> So Q cannot be multiple of any of the numbers in the list, thus Q is prime.
> I found
> that the largest known prime number is 2^74,207,281 − 1 which has
> 22,338,618 digits.
> I found also a list of the first fifty million primes
> <https://primes.utm.edu/lists/small/millions/>. If we multiply all the
> numbers in this list, it will yield a number that has much more than 50
> million digits and thus ought be much larger than the currently known
> largest prime number.
> Please help!!! Where is the catch? It cannot be that simple!
As I understand it your list of primes grows as you find new primes.
Problem is your solution is not finding all the primes between the last
prime in the list and the new prime you've just discovered. The next
prime you compute will not include these missing primes.
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