 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 2 of degree 2
x ^ 2 + x + 1, 2
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 2 of degree 17
x ^ 17 + x ^ 3 + 1, 2
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 2 of degree 43
x ^ 43 + x ^ 6 + x ^ 4 + x ^ 3 + 1, 2
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 2 of degree 62
x ^ 62 + x ^ 6 + x ^ 5 + x ^ 3 + 1, 2
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 3 of degree 30
x ^ 30 + x + 2, 3
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 5 of degree 22
x ^ 22 + x ^ 2 + x + 3, 5
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 7 of degree 16
x ^ 16 + 2 x + 3, 7
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 17 of degree 14
x ^ 14 + x ^ 2 + 2 x + 6, 17
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 137 of degree 7
x ^ 7 + x + 3, 137
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 223 of degree 8
x ^ 8 + x + 51, 223
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 557 of degree 6
x ^ 6 + x + 5, 557
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 2 of degree 4
x ^ 4 + x + 1, 2
Confirming polynomial is primitive with a brute force check.
WARNING: You may wait an impossibly long time!
To abort, hit controlC in your console window to stop this program.
x ^ 4 + x + 1, 2 confirmed primitive!
+ OperationCount 

 Integer factorization: Table lookup + Trial division + Pollard Rho

 Number of trial divisions : 0
 Number of gcd's computed : 0
 Number of primality tests : 0
 Number of squarings: 0

 Polynomial Testing

 Total num. degree 4 poly mod 2 : 16
 Number of possible primitive poly: 2
 Polynomials tested : 4
 Const. coeff. was primitive root : 2
 Free of linear factors : 1
 Irreducible to power >=1 : 1
 Had order r (x^r = integer) : 1
 Passed const. coeff. test : 1
 Had order m (x^m != integer) : 1

+
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
Primitive polynomial modulo 3 of degree 5
x ^ 5 + 2 x + 1, 3
Confirming polynomial is primitive with a brute force check.
WARNING: You may wait an impossibly long time!
To abort, hit controlC in your console window to stop this program.
x ^ 5 + 2 x + 1, 3 confirmed primitive!
+ OperationCount 

 Integer factorization: Table lookup + Trial division + Pollard Rho

 Number of trial divisions : 0
 Number of gcd's computed : 0
 Number of primality tests : 0
 Number of squarings: 0

 Polynomial Testing

 Total num. degree 5 poly mod 3 : 243
 Number of possible primitive poly: 22
 Polynomials tested : 8
 Const. coeff. was primitive root : 3
 Free of linear factors : 1
 Irreducible to power >=1 : 1
 Had order r (x^r = integer) : 1
 Passed const. coeff. test : 1
 Had order m (x^m != integer) : 1

+
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
There are 6 primitive polynomials modulo 2 of degree 5
Primitive polynomial modulo 2 of degree 5
x ^ 5 + x ^ 2 + 1, 2
Primitive polynomial modulo 2 of degree 5
x ^ 5 + x ^ 3 + 1, 2
Primitive polynomial modulo 2 of degree 5
x ^ 5 + x ^ 3 + x ^ 2 + x + 1, 2
Primitive polynomial modulo 2 of degree 5
x ^ 5 + x ^ 4 + x ^ 2 + x + 1, 2
Primitive polynomial modulo 2 of degree 5
x ^ 5 + x ^ 4 + x ^ 3 + x + 1, 2
Primitive polynomial modulo 2 of degree 5
x ^ 5 + x ^ 4 + x ^ 3 + x ^ 2 + 1, 2
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Error. Polynomial has bad syntax or coefficients are out of range. [ Error in parser converting polynomial from string x 1 for p = 2 Expecting to see x^ or x or x ^ integer in sentence x 1 ]
This program generates primitive polynomials of degree n modulo p.
Usage: Generate a single random polynomial of degree n modulo p where p is a prime >= 2 and n is an integer >= 2
Primpoly p n
Example:
Primpoly 2 4
Selfcheck passes...
Primitive polynomial modulo 2 of degree 4
x ^ 4 + x + 1, 2
Usage: Test whether a polynomial is primitive modulo p.
Primpoly t , p
If you leave off the modulus p we default to p = 2
Examples:
Primpoly t x^4 + x + 1, 2
Selfcheck passes...
x ^ 4 + x + 1, 2 is primitive!
Primpoly t x^4 + x + 1
Selfcheck passes...
x ^ 4 + x + 1, 2 is primitive!
Usage: Generate all primitive polynomial of degree n modulo p.
Primpoly a p n
Example:
Primpoly a 2 4
Selfcheck passes...
Primitive polynomial modulo 2 of degree 4
x ^ 4 + x + 1, 2
Primitive polynomial modulo 2 of degree 4
x ^ 4 + x ^ 3 + 1, 2
Usage: Same but show computation statistics.
Primpoly s p n
Examples:
Primpoly.exe s 13 19
Selfcheck passes...
Primitive polynomial modulo 13 of degree 19
x ^ 19 + 9 x + 2, 13
+ OperationCount 

 Integer factorization: Table lookup + Trial division + Pollard Rho

 Number of trial divisions : 0
 Number of gcd's computed : 9027
 Number of primality tests : 2
 Number of squarings: 9026

 Polynomial Testing

 Total num. degree 19 poly mod 13 : 1461920290375446110677
 Number of possible primitive poly: 6411930599771980992
 Polynomials tested : 120
 Const. coeff. was primitive root : 46
 Free of linear factors : 11
 Irreducible to power >=1 : 1
 Had order r (x^r = integer) : 1
 Passed const. coeff. test : 1
 Had order m (x^m != integer) : 1

+
Usage: Print help message.
Primpoly h
Primitive polynomials find many uses in mathematics and communications
engineering:
* Generation of pseudonoise (PN) sequences for spread spectrum
communications and chip fault testing.
* Generating Sobol sequences for high dimensional numerical integration.
* Generation of CRC and Hamming codes.
* Generation of Galois (finite) fields for use in decoding ReedSolomon
and BCH error correcting codes.
For detailed technical information, see my web page
http://seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/overview.html
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
x ^ 4 + x + 1, 2 is primitive!
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
x ^ 3 + x + 2, 3 is NOT primitive!
 A Program for Computing Primitive Polynomials.
Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
GNU General Public License. This is free software, and you are welcome
to redistribute it under certain conditions; see the GNU General Public License
for details.
Selfcheck passes...
x ^ 2 + x + 10, 32749 is primitive!