20220914, 06:22  #12 
"特朗普trump"
Feb 2019
朱晓丹没人草
132_{10} Posts 

20220914, 07:03  #13 
"Curtis"
Feb 2005
Riverside, CA
2^{3}×3×5×47 Posts 
If you have such strong opinions about all this, why are you asking us what to run?
Define "better". Faster? False positives don't matter beyond a couple hundred digits, and if your interests are under 500 digits then speed doesn't matter for what software you pick you should pick the one you can use without asking 30 questions where you argue with the answers. 
20220914, 08:13  #14  
"特朗普trump"
Feb 2019
朱晓丹没人草
2^{2}×3×11 Posts 
Quote:
pfgw output  PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] ***WARNING! file input2 may have already been fully processed. Primality testing 999998912894617 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 5, base 5+sqrt(5) 999998912894617 is prime! (0.0011s+0.0006s) Done.  it tell me that 999998912894617 is a prime！ but 5085473*196638329=999998912894617=(3*m  1) (116*m + 1),where m=1695158 BUG!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Last fiddled with by bbb120 on 20220914 at 08:21 

20220914, 08:27  #15 
Mar 2006
Germany
3,001 Posts 
How you call pfgw64?
I got Code:
>pfgw64 q999998912894617 PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] Switching to Exponentiating using GMP 999998912894617 is composite: RES64: [0003827DA76C6B9C] (0.0001s+0.0033s) 
20220914, 08:30  #16  
"特朗普trump"
Feb 2019
朱晓丹没人草
204_{8} Posts 
Quote:
Code:
pfgw tp input2 so It must be a BUG! 

20220914, 12:39  #17 
"Mark"
Apr 2003
Between here and the
2·3^{4}·43 Posts 
Before you do a primality test you should search for factors then run a PRP test.
Although f doesn't find a factor, f10000 does. Code:
pfgw64 f10000 tp q999998912894617 Cverbose PFGW Version 4.0.0.64BIT.20190330.Win_Dev [GWNUM 29.7] Factoring numbers to 10000% of normal. Primality testing 999998912894617 [N+1, BrillhartLehmerSelfridge] trial factoring to 10000000 factors: 5085473*196638329 999998912894617 is factored (0.0736s+0.0001s) tc and tm show composite. I see that tp shows prime, but the number being tested does not meet the conditions that are necessary for the test output to be valid. tm is used for numbers of the form k*b^n+1. tp is used for numbers of the form k*b^n1. 
20220914, 12:40  #18  
Feb 2017
Nowhere
13·479 Posts 
I see two possibilities here. One is, you don't know the definition of "prp test." The other is, you are feigning an ignorance you do not own. Either way, it looks like trolling to me.
Quote:
I ran this test two different ways in PariGP for n=999998912894617 (which is congruent to 2 (mod 5)) and got the same answer. It isn't 20 Mod N. The test shows N is composite. ? n=999998912894617;r1=Mod(Mod(1,n)*x,x^210*x+20)^(n+1);print(lift(r1)) Mod(988864715305694, 999998912894617) ? n=999998912894617;r2=Mod(Mod(1,n)*(2*x+4),x^2x1)^(n+1);print(lift(r2)) Mod(988864715305694, 999998912894617) 

20220915, 01:04  #19  
"特朗普trump"
Feb 2019
朱晓丹没人草
84_{16} Posts 
Quote:
Code:
Clear["Global`*"];(*Clear all variables*) (*计算calculate:(a+b*sqrt(x))^m mod n*) QuadraticMod[a_,b_,x_,m_,n_]:=Module[ {aa,bb,kk,m2}, m2=IntegerDigits[m,2];(*把m写成二进制的方式*) {aa,bb}={1,0};(*初始值*) Do[ {aa,bb}=Mod[{aa*aa+bb*bb*x,2*aa*bb},n];(*(aa+bb*sqrt(x))^2 mod n*) If[m2[[kk]]==1, {aa,bb}=Mod[{aa*a+bb*b*x,aa*b+a*bb},n](*(aa+bb*sqrt(x))*(a+b*sqrt(x)) mod n*) ], {kk,1,Length@m2}]; Return[{aa,bb}](*output输出结果*) ] Code:
n=999998912894617; QuadraticMod[5,1,5,n+1,n] {988864715305694, 0} the same result with you. so It must be a bug in pfgw! 

20220915, 02:28  #20  
"特朗普trump"
Feb 2019
朱晓丹没人草
2^{2}·3·11 Posts 
Quote:
Code:
n=803837457453639491257079614341942108138837688287558145837488917522\ 2974273765333652186502336163960045457915042023603208766569966760987284\ 0439654082329287387918508691668573282677617710293896977394701670823042\ 8687109997439976544144845341155872450633409279022275296229414984230688\ 1685404326457534018329786111298960644845216191652872597534901 Code:
pfgw b2 input3.txt Code:
***WARNING! file input3.txt may have already been fully processed. 80383745745363949125......7534901 is 2PRP! (0.0021s+0.0001s) Done. Code:
pfgw b14 input3.txt Code:
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] ***WARNING! file input3.txt may have already been fully processed. 80383745745363......72597534901 is 14PRP! (0.0016s+0.0001s) Done. 14^((n1)/4)mod n not equal ±1 and 14^((n1)/2)mod n equal 1 (not equal 1), thus,miller rabin tell us that n must be a composite number but,pfgw tell us n is 14PRP so pfgw must use fermat test as "prp test",not millerrabin. 

20220915, 02:30  #21  
"特朗普trump"
Feb 2019
朱晓丹没人草
84_{16} Posts 
Quote:
Code:
but the number being tested does not meet the conditions that are necessary for the test output to be valid 

20220915, 03:15  #22 
"Curtis"
Feb 2005
Riverside, CA
2^{3}×3×5×47 Posts 
A "bug" is unexpected behavior. Using a primality test that isn't known to be correct on your input is not a bug.
You don't understand the software, and you're mistaken about having found a bug. Maybe ease up on the accusations until you understand what the various pfgw flags and tests do? 
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