what is the best primality software?

[bbb120]

Originally Posted by Dr Sardonicus

Please explain the warning about input3.txt

FWIW I verified that n "passes" the Fermat PRP tests to base 2 and base 14.

When n tests as a Fermat PRP but as composite by Miller-Rabin to the same base, a factorization is immediately obtainable.

In the case at hand, we have the factors

p=2004791083197498027091532260422734265025940830205662543872531023690016085350598121358111595798609866791081582542679083484572616906958584643763990222898400226296015918301

and q = 2*p - 1,

q = 4009582166394996054183064520845468530051881660411325087745062047380032170701196242716223191597219733582163165085358166969145233813917169287527980445796800452592031836601

EDIT:
It means you've been using the wrong tool for the job. And then you've been complaining that the problem is that the tool is broken.

I know its factor ,
let x=14^((n-1)/4)mod n ,x not equal ±1
and x^2=14^((n-1)/2)mod n equal 1,
so GCD(x-1,n) and GCD(x+1,n) will give the factor of n!

[rogue]

Originally Posted by bbb120

what does "F-Strong test" mean in pfgw?

Per pfgwdoc.txt:

A.3.4 F-Strong test
   This test is used when you use the -t option, and your factors don't reach
   the magic 33.33%. It is a strong-primality test, and gives more certainty
   than a Fermat test, but still is NOT a proof!

[bbb120]

Originally Posted by rogue

Per pfgwdoc.txt:

A.3.4 F-Strong test
   This test is used when you use the -t option, and your factors don't reach
   the magic 33.33%. It is a strong-primality test, and gives more certainty
   than a Fermat test, but still is NOT a proof!

I need more explanation on the test ,I need more detail about it .
I know it (pfgwdoc.txt),and I read it before

[VBCurtis]

Try a search engine. Again.

Your combination of complaints, demands, and abrasiveness (impoliteness) is growing quite tiresome.

[bbb120]

Originally Posted by VBCurtis

Try a search engine. Again.

Your combination of complaints, demands, and abrasiveness (impoliteness) is growing quite tiresome.

I know search engine !
I also know about search engines too,
but I didn't find any valuable information!

[bbb120]

why PFGW use fermat test ,not miller rabin test ?
for what reason to use fermat test instead of miller rabin test ?

Moderator note: I moved this post and all responses from new thread to this thread.

[bbb120]

fermat test is useless for Carmichael number!

[paulunderwood]

Originally Posted by bbb120

why PFGW use fermat test ,not miller rabin test ?
for what reason to use fermat test instead of miller rabin test ?

OpenPFGW is open source. You are welcome to alter the source to provide Miller-Rabin tests. Do it instead of starting more threads about how inadequate the program is for your needs.

[paulunderwood]

Originally Posted by bbb120

fermat test is useless for Carmichael number!

Miller-Rabin is "useless" with some composites. So what? Use Fermat+Lucas, and if you want to be 100% of primality use something like ECPP (if your number is general enough and not of a special form).

[Denial140]

https://en.wikipedia.org/wiki/Carmic...r#Distribution

[retina]

Originally Posted by bbb120

why PFGW use fermat test ,not miller rabin test ?
for what reason to use fermat test instead of miller rabin test ?

If this upsets you too much then you can ask for your money back, and move to a different product that has tests you find more to your liking.

Alternatively, if no product suits your desires then you may need to write your own testing code.

Hope that helps.