piclist 2017\09\06\122744a >
www.piclist.com/techref/index.htm?key=prime+numbers
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 âˆ’ 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.

Cheers,

Isaac

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