"New" primality test/check

[gophne]

I think that I might have discovered a new "primality" test, as well as a new prime sieve. I think that the primality test might be computer-time friendly as well, as it consists of a simple straight calculation/logic test only. I think it is big. What would be the most appropriate route to submit it to the math community for scrutiny?

[CRGreathouse]

The usual way to announce a mathematical discovery is to write a paper, push a preprint to the arXiv, then publish the paper. In the fortunate case that the algorithm can be coded easily I would recommend programming a reference implementation and including the timing results in the preprint and paper. If they improve on the current state of the art, it might be worth posting a note to NMBRTHRY while you're writing the paper. (Since you're here, you could also post timings here; depending on what they are we could advise further.)

[gophne]

Thanks CRGreathouse.

I had previous attempts at prime innovation on this site, with a bit of embarrassing results!

I am a hobbyist only, and have made some interesting discoveries (using hobbyist approach of "go where my fancy takes me"). I think my present "test" is indeed interesting and had not found anything like it in the "primality" literature, especially on the internet as well -not to say that it is unique/new, but submitting it would of course quickly verify the authenticity of the system/test in a split second.

I was thinking of submitting the "test" on this forum, but I could write a "paper" as I can ask my son/daughter (who is more competent w.r.t writing academic papers) to assist if required.

I am really exited, but it could of course turn out to be a damp squib as well.

Thanks for the initial advise.

[CRGreathouse]

Originally Posted by gophne

I had previous attempts at prime innovation on this site, with a bit of embarrassing results!

In that case I'd suggest doing the same again: show what you have and let the forum give feedback. If it's good they can give you advice on how to prepare the work for publication, if not you're saved the effort and possible embarrassment.

Here are some things we (and others) would likely be interested in checking:

• Is the description clear enough that we can understand the intended algorithm?
• Does it classify all primes as prime?
• Does it classify all composites as composite?
• Does it run in reasonable time on average primes?
• Does it run in reasonable time on worst-case primes?
• Can you prove the above claims?
• Is the algorithm easy to implement?

[rogue]

Can you write a computer algorithm to execute the test? If so, have you tested it against known primes and composites? Do you know how fast/slow the test is compared to other primality tests? Can it be used as a primality test for numbers of any form?

[gophne]

Hi CRGreathouse

The algorithm is very clear.
ALL primes are covered- tested to M34 -2^1,257,787-1, Seriously!
ALL composites are identified!
Time O(log n) -Very very fast. Serious.
ALL primes are defined -NO false primes expected as per algorithm logic.
The algorith is a logical formulation, so can be verified quickly.
If authenticated, will compare to simplicity of Euclid's Proof for Infinite number of Primes.
If true, will be a new frontier in PNT

Call me crazy

[chalsall]

Originally Posted by gophne

The algorithm is very clear.

Under US of A law, an algorithm cannot be patented. So, you are unlikely to make any money from this discovery directly.

On the other hand, this would be a ground breaking discovery if it was true.

Why don't you give us the algorithm so the experts here can vet it?

[gophne]

Hi Rogue

Yes, I run the algorithm in SAGE. Time, is the time needed in SAGE to caculate straight math formula/logic test, of course involving very large numbers. I tested M34 -2^1,257,787-1. I won't mention the time taken as I will be debarred from this site. (I use a Intel(R) Core(TM)2 CPU T5500 @ 1.66 GHz 1.67 GHz RAM 2.00 GB, 64 bit O/S x64 based processor).

I have tested it to M34. If vindicated, the algorithm will replace GIMP. (Your are allowed to scream out in vexation at this point w.r.t the claims I am making...I don't expect anybody to consider my claims seriously at this stage -I am looking for the best way to submit my algorith/system

Tests ALL known Primes...it is that surreal.

The algorithm maps ALL primes in sequence.

Now you can release your breath and burst out laughing!!!

[gophne]

Originally Posted by chalsall

Under US of A law, an algorithm cannot be patented. So, you are unlikely to make any money from this discovery directly.

On the other hand, this would be a ground breaking discovery if it was true.

Why don't you give us the algorithm so the experts here can vet it?

Hi Chalsall

That was my intention, to submit the algorithm to the world on this site, with the advantage that the algorithm will be ripped to pieces in a matter of micro seconds, if it is a hoax, with myself probable banned for life from this site, if not any other serious math site.

However, I would like to believe that a Site such as this would be able to offer me some sort of protection of my work/intellectual property, even if is open source.

If the algorithm is confirmed, this would have a serious implication on Prime Number Theory.

This is my dilemma.

[gophne]

Post erased as it was a duplicate of #9. Apologies.

[guptadeva]

Originally Posted by gophne

What would be the most appropriate route to submit it to the math community for scrutiny?

the mathematical community was the first scientific group to understand, that classical publications in books, journals or other printed media has limits.

you could always publish your results in arxiv (https://arxiv.org/help/submit) and/or here in mersenneforum where the density of prime experts is very high and where you would get deep and quick feedback needed to determine the future of your new primality check ...