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Thread: Prime numbers
www.piclist.com/techref/index.htm?key=prime+numbers
picon face BY : Isaac M. Bavaresco email (remove spam text)


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
(Wikipedia:<https://en.wikipedia.org/wiki/Largest_known_prime_number>)
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!


Cheers,

Isaac




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