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Old 2022-09-13, 05:39   #1
bbb120
 
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Default what is the best primality software?

I only know mathematica or maple to test primality on a giving number !
but mathematica is too large !
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Old 2022-09-13, 13:06   #2
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Quote:
Originally Posted by bbb120 View Post
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.
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Old 2022-09-14, 00:29   #3
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Quote:
Originally Posted by rogue View Post
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!
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Old 2022-09-14, 01:29   #4
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Pick a program (say PFGW) that does a prp test, then once you find a probable prime use ECPP software to prove it prime.
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Old 2022-09-14, 02:42   #5
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Originally Posted by VBCurtis View Post
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"?
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Old 2022-09-14, 03:21   #6
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Quote:
Originally Posted by VBCurtis View Post
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

Last fiddled with by bbb120 on 2022-09-14 at 03:22 Reason: improve
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Old 2022-09-14, 04:11   #7
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Code:
./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.

Last fiddled with by paulunderwood on 2022-09-14 at 04:13
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Old 2022-09-14, 05:35   #8
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Quote:
Originally Posted by paulunderwood View Post
Code:
./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?
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Old 2022-09-14, 05:52   #9
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Quote:
Originally Posted by bbb120 View Post
how pfgw know it is a composite number with -tc option?
If it fails that test with -tc option, it is composite.
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Old 2022-09-14, 05:55   #10
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Quote:
Originally Posted by rogue View Post
That depends upon the numbers you want to test. Please provide more details.
what does "F-Strong test" mean in pfgw?
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Old 2022-09-14, 06:09   #11
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Quote:
Originally Posted by VBCurtis View Post
If it fails that test with -tc option, it is composite.
I want to know why,or the algorithm behind it!

Last fiddled with by bbb120 on 2022-09-14 at 06:10
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