Is there a formula for generating prime numbers and proving their primality?

[a1call]

The following 183 digit prime was found using formulation using the Theorem 1, without scripting and programming.
Is that of any significance considering the method?
Are there any other formulas which can give comparable results without programming?

The number of digits is about a dozen less than the maximum of what the free version of Wolfram Alpha accepts.

268247424057311445389468276509855422892624146761442207989329055956776521156436821116123624436462260510842892838582894073662704750945426649505938377042214898386145890456554863200575291

http://www.wolframalpha.com/input/?...77042214898386145890456554863200575291+prime?Credits to Wolfram Alpha for doing the arithmetic.

Thank you for your time and replies.

 

[mfb]

What were the base numbers you used, which two numbers did you use to come to this difference?

The number is prime.

 

[a1call]

What were the base numbers you used, which two numbers did you use to come to this difference?

The number is prime.

I used a probable prime concept using Theorem 1 rather than a proven prime.
I will PM the exact expression shortly.

 

[micromass]

The following 183 digit prime was found using formulation using the Theorem 1, without scripting and programming.
Is that of any significance considering the method?
Are there any other formulas which can give comparable results without programming?

The number of digits is about a dozen less than the maximum of what the free version of Wolfram Alpha accepts.

268247424057311445389468276509855422892624146761442207989329055956776521156436821116123624436462260510842892838582894073662704750945426649505938377042214898386145890456554863200575291

http://www.wolframalpha.com/input/?i=268247424057311445389468276509855422892624146761442207989329055956776521156436821116123624436462260510842892838582894073662704750945426649505938377042214898386145890456554863200575291+prime?Credits to Wolfram Alpha for doing the arithmetic.

Thank you for your time and replies.

Please tell us in detail how you found this number, or tell us how to replicate this result.

 

[a1call]

Please tell us in detail how you found this number, or tell us how to replicate this result.

As I mentioned before this is based on prime candidacy and not proof so the sum does not converge to less than square of the largest prime or integer in factorial.

A few notes:

* This was an exercise to see the capabilities of the free version of Wolfram Alpha
* The free version of Wolfram Alpha can actually calculate much (much) larger prime candidates but the problem is you can't feed it back for the tool to see if it is a prime. The Pro version can input much larger numbers. So if anyone has the Pro account and comes up with larger primes using the Teorem 1, please feel free to post it here.
* I would have used multifactorials (which does not require knowing all the lower primes used) rather than primorials, but "off the shelf" Wolfram alpha does not support multifactorials higher than double factorials.
* Number of prime numbers below a number can be calculated, though I haven't bothered doing:

https://en.wikipedia.org/wiki/Prime_number#Number_of_prime_numbers

The point of posting the prime is to suggest that Theorem 1 might perhaps be of some value since it can come up with primes with relatively few trials for large numbers even without converging to less than the square of the largest prime. It is certainly more probable than Mersenne primes which in fact are quite rare. As pointed out on the other board there are other formulas that can give large prime candidates. But I would argue The Theorem 1 approaches will give much more probable primes than those.

* For the record I am still of the opinion that there is enough information in this thread for someone with better math skills than myself to come up with a mathematical expression evaluating to more than a billion digits and the proof that it is a prime and can probably fit all that in a single standard sheet of paper, I have not seen any arguments on the two boards or the PMs on them to convince me otherwise.

* To replicate or come up with other primes please adjust the 2 primorials in the example below to optimize for the closest sum to the square of the largest prime factor and largest number of digits. it took me more trials to come of with the free version input limitation than with the 1st prime.** here is the exact mathematical expression:

http://www.wolframalpha.com/input/?i=((+primorial+150))/(primorial+85)-(1*primorial+85)&f=1

 

[micromass]

http://www.wolframalpha.com/input/?i=((+primorial+150))/(primorial+85)-(1*primorial+85)&f=1

And you actually think you will find a billion digit prime number with this?

 

[a1call]

And you actually think you will find a billion digit prime number with this?

You asked me a question and I answered it. If you chose to ignore what I said, then there is no point in replying is there?

 

[micromass]

You asked me a question and I answered it. If you chose to ignore what I said, then there is no point in replying is there?

Well, I don't see the point of this thread anyway...

 

[Ryan_m_b]

Closed pending moderation

 

[mfb]

To check numbers with more digits, you can use tools like this. It can identify primes that size within less than a minute.

Anyway, it's not a method to find billion-digit primes.

Edit: Sorry, didn't see the previous post, the thread was still displayed as open.