Further Proof, There are an Infinite Number of Prime

If we let p stand for any prime. And we let p! be the product of all the naturals from 1 to p, then p!+1 shall be a product of a prime larger than p, as it's smallest factor.

I would think that there is infinite numbers so there are infinite primes. Same would be for perfect numbers too right?

Also after some point don’t primes get more common?

I may be uneducated though.

Thank you, Once again for your input in my threads.

To Answer your question about "Perfect Numbers."

It is not known whether there are infinitely many perfect numbers, nor whether there are infinitely many Mersenne primes. As a side note, there are names for non-perfect numbers: if the sum of a number's proper factors are less than the number, it's a deficient number.

Because every time there is a new prime, that is one more way that subsequent numbers can fail to be prime. After 2, there is a 1/2 chance that a number won't divide by 2; after 3, there is a 2/3 chance a number won't divide by 3 leaving a (1/2)(2/3)=1/3 chance of not dividing by either 2 or 3; after 5 there is a (1/2)(2/3)(4/5)=4/15 chance; and the chance of new primes must always keep shrinking.

You mean, "Uninformed".

Not, so anymore.

Read two years on any subject and you have the equivalent of a Master's Degree. I have 714. I gained 23.8 degrees every two years for 60 years. But check my math. Now I have a lot of experiments and research to finish. I'll be a Professor by the time I'm 97. Woohoo! Love the Primes. You only have to divide by primes as you go up to determine if the number is Prime. Again, I'll have to do a review. Euclid's Theorem. I use to hang out on Euclid Street in St. Louis. It was the cool part of town. Had a glassblower you could watch and cool stores. Not named after Euclid.

I've been playing with Geodesic Dome calculations. There's some interesting stuff. You can't just join a bunch of equal area triangles together. You have to engineer it with some 5 sided, some 6 sided panels (which the 6 sided would be six triangles). There are various ways they've gotten around it and each dome seems unique. Buckminster Fuller is the one who brought this to our attention back in the 70's in the Whole Earth Catalog. Enjoy.