GQQ: a "deterministic" "primality" test in O(ln n)^2

[Chair Zhuang]

I'm not good at English. Can you take a example,or say it in other words.

[CRGreathouse]

Originally Posted by science_man_88

So basically a suped up fermat test. p-1 factors into them all last I checked.

sm, if you are able to understand the algorithm I'd appreciate an explanation. Reading your post and then CZ's I get the impression it's something like a base-16644 pseudoprime test, but if you could give more details that would be great.

(Of course this might not be possible!)

[Chair Zhuang]

I'm not good at English. Can you take a example or say it in other words.

[Chair Zhuang]

As you say I would not to say the detail currently. If GQQ is a base-16644 pseudoprime test, it can not test Carmichael numbers, but it has done it.

[science_man_88]

Originally Posted by CRGreathouse

sm, if you are able to understand the algorithm I'd appreciate an explanation. Reading your post and then CZ's I get the impression it's something like a base-16644 pseudoprime test, but if you could give more details that would be great.

(Of course this might not be possible!)

I know the following:

1) they try relating it to Fermat's sequence (thought they meant fermats test)
2) they use polynomials that divide by p-1
3) they made me think it was a suped up fermat test.

[ryanlatterell]

All the factors, all at once, every time, guaranteed

[CRGreathouse]

Originally Posted by Chair Zhuang

As you say I would not to say the detail currently. If GQQ is a base-16644 pseudoprime test, it can not test Carmichael numbers, but it has done it.

Agreed.

It seems you have found a pseudoprimality test. It might even be a real primality test, but without a proof we couldn't know. (Technically, we can't even be sure it's a pseudoprimality test but I'll give you the benefit of the doubt there.)

[Chair Zhuang]

To CRGreathouse
I agree what you said. In Mathematically, 10^10 or more concrete test is not better

than only one abstract proof.
Your doubt is reasonable. Maybe, we would think GQQ is only a database. But if it is

so my computer must has a very big hard disk or I must spend much money to rent

cloud drive to store the primes. And on the other hand, how did I obtain these

primes?
Acording to the prime number theory there are about 2^10000/ln(2^10000)=

(about)10^3000 primes from 2 to 2^10000 in the database.

[CRGreathouse]

Originally Posted by Chair Zhuang

Your doubt is reasonable. Maybe, we would think GQQ is only a database.

No, as you say, there are too many numbers to store. Much more likely is a pseudoprime test. You wouldn't need much space or a powerful machine to pull that off.

And if it is a novel test, congrats -- though you're certainly not the first, it's not every day you see a new pseudoprimaliy test pop up, and it's only the second one I can think of being announced here on these forums (the other being the Vrba-Reix test).

[Chair Zhuang]

To CRGreathouse
Thank you for your congratulations.
Can you tell me the way to Vrba-Reix test?
Let's see the words below on 2018/3/19 again.
In GQQ primality test:
______________________________________________________________________________________
.p=40751 base 16644: 1,17409,10638,36705,3788,..... The value numbers are

59568 and 59568 at item (40751+1)/2 and next.
q=122251 base 16644: 1,83349,83494,74553,56287,...... The value

numbers are 1 and 83349 at item (122251+1)/2 and next.
_______________________________________________________________________________________
p=40751 is using a right base, so we can decide its primality. And
q=122251 is'nt using a right base, and "the value number is also 1 at item

(122251-1)/2. This sequence is LIKELY a Fermat sequence, but is'nt really Fermat

sequence." (Giving it a right base, its sequence is really Fermat sequrnce.)
To a prime number we can give it a right base by its form of the number , and

decide its primality. If a number is the form as a prime is and the value numbers at

item (n+1)/2 and next are not correct, the number is composite.
GQQ is single algorithm and its sequence, Quifu sequence, contains Fermat

sequence, but determining primality is'nt by Fermat sequence.

[CRGreathouse]

Originally Posted by Chair Zhuang

Can you tell me the way to Vrba-Reix test?

Many of the bits and pieces have been collected together here:
https://trex58.wordpress.com/math2matiques/