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Old 2020-08-02, 01:44   #1
amenezes
 
Aug 2020

916 Posts
Default Solovay Strassen Mod

In the Solovay strassen primality test we can can make the the base a=2 and another a or b such that the jacobi symbol is the opposite sign of that of the jacobi of 2 with respect to n the odd composite number which we need to determine the primality of. Please comment on the paper I attached and the algorithm in pseudo code.
Thank you,
Allan
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File Type: pdf sstest.pdf (142.0 KB, 108 views)
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Old 2020-08-02, 05:54   #2
amenezes
 
Aug 2020

32 Posts
Default This is empirically true only so far

This is only empirically determined to be true for all base 2 Euler pseudo primes uptil 2^64-1 but the proof given is not correct as it includes circular reasoning. My stupid error in posting it up. But the algorithm described there seems to be empirically correct. If any one else could find a reasonable proof it would be good.
Sorry,
Allan
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Old 2020-08-02, 06:07   #3
amenezes
 
Aug 2020

32 Posts
Default

Attached is the code I tested it with in C. It uses GMPLIB http://gmplib.org
Compile it as :
gcc -o pspf -lm -m64 -lgmp pspfactorsm.c
and run :
./pspf filename.out filename,in
where filename.in = psps-below-2-to-64.txt
The file psps-below-2-to-64.txt is unput to the program and filename.out is the output file.
The file psps-below-2-to-64.txt can be found at the following URL:

http://www.cecm.sfu.ca/Pseudoprimes/


Decompress the file and use it.
Thank you,
Allan
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File Type: c pspfactorsm.c (2.0 KB, 105 views)
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Old 2020-08-02, 06:55   #4
amenezes
 
Aug 2020

32 Posts
Default

Soory the correct code is here. The former code has j=0. It should be j=ja;
Thank you.
Allan
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File Type: c pspfactorsm.c (1.8 KB, 109 views)
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Old 2020-08-02, 17:20   #5
amenezes
 
Aug 2020

32 Posts
Default

In the Theorem proof the error is here:
2^(n-1)==1 ( mod n) = 1 (mod p) as p | n
b^(n-1)==1( mod n) == 1 (mod p) as p | n
Subtracting the two equivalences gives:
2^(n-1)==b^(n-1) ( mod p)
Taking the square roots of both sides gives:
2((n-1)/2)==+/- b^((n-1)/2)( mod p)
and not
2^((n-1)/2) == b^((n-1)/2) (mod p)
as claimed in the proof.
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