what is the best primality software?

[bbb120]

I only know mathematica or maple to test primality on a giving number !
but mathematica is too large !

[rogue]

Originally Posted by bbb120

I only know mathematica or maple to test primality on a giving number !
but mathematica is too large !

That depends upon the numbers you want to test. Please provide more details.

[bbb120]

Originally Posted by rogue

That depends upon the numbers you want to test. Please provide more details.

for any integer to test primality ,not for special type of integer!

[VBCurtis]

Pick a program (say PFGW) that does a prp test, then once you find a probable prime use ECPP software to prove it prime.

[bbb120]

Originally Posted by VBCurtis

Pick a program (say PFGW) that does a prp test, then once you find a probable prime use ECPP software to prove it prime.

PFGW，where can I download it?
maybe I can use random miller rabin to "prove" it prime.
does PFGW support random miller rabin base to "prove"?

[bbb120]

Originally Posted by VBCurtis

Pick a program (say PFGW) that does a prp test, then once you find a probable prime use ECPP software to prove it prime.

I download pfgw from http://www.fermatsearch.org/download.php

but in pfgwdoc.txt
-------------------------------------
-b Change base for prp-testing.
This switch requires and argument
Some numbers will be prp, even if it isn't a prime. You may want to
try several bases.
Base should be between 2 and 255
Example: pfgw -b7
-------------------------------------
2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867

this 397-digits composite pass all base(2 to 306)miller rabin test,
so this software should not give a limition to the choosing of base!!!


2887148238050771212671429597130393991977609459279722700926516024197432\
3037991527331163289831446392259419778031109293496555784189494417409338\
0561511397999942154241693397290542371100275104208013496673175515285922\
6962916775325475044445856101949404200039904432116776619949629539250452\
6987193290703735640322737012784538991261203092448414947289768854060249\
76768122077071687938121709811322297802059565867

[paulunderwood]

./pfgw64 -tc -q2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867 [N-1/N+1, Brillhart-Lehmer-Selfridge]                                    
Running N-1 test using base 2                                                  
Factored: 10475096971045985224204423648945582453962513105348124302901261662540724079869634880456766224539126779375883658239075983560088580357347                                    
2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867 is composite (0.0115s+0.0011s)

There are no known composite numbers that pass PFGW's Fermat+Lucas which can be achieved by running the combined N+1/N-1 tests with the switch -tc.

[bbb120]

Originally Posted by paulunderwood

./pfgw64 -tc -q2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867 [N-1/N+1, Brillhart-Lehmer-Selfridge]                                    
Running N-1 test using base 2                                                  
Factored: 10475096971045985224204423648945582453962513105348124302901261662540724079869634880456766224539126779375883658239075983560088580357347                                    
2887148238050771212671429597130393991977609459279722700926516024197432303799152733116328983144639225941977803110929349655578418949441740933805615113979999421542416933972905423711002751042080134966731755152859226962916775325475044445856101949404200039904432116776619949629539250452698719329070373564032273701278453899126120309244841494728976885406024976768122077071687938121709811322297802059565867 is composite (0.0115s+0.0011s)

There are no known composite numbers that pass PFGW's Fermat+Lucas which can be achieved by running the combined N+1/N-1 tests with the switch -tc.

how pfgw know it is a composite number with -tc option?

[VBCurtis]

Originally Posted by bbb120

how pfgw know it is a composite number with -tc option?

If it fails that test with -tc option, it is composite.

[bbb120]

Originally Posted by rogue

That depends upon the numbers you want to test. Please provide more details.

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

[bbb120]

Originally Posted by VBCurtis

If it fails that test with -tc option, it is composite.

I want to know why,or the algorithm behind it!