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.

Please help!!! Where is the catch? It cannot be that simple!

Cheers,

Isaac

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