 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.
Primitive polynomial modulo 2 of degree 2
x ^ 2 + x + 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.
Primitive polynomial modulo 2 of degree 17
x ^ 17 + x ^ 3 + 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.
Primitive polynomial modulo 2 of degree 43
x ^ 43 + x ^ 6 + x ^ 4 + x ^ 3 + 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.
Primitive polynomial modulo 2 of degree 62
x ^ 62 + x ^ 6 + x ^ 5 + x ^ 3 + 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.
Primitive polynomial modulo 3 of degree 30
x ^ 30 + x + 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.
Primitive polynomial modulo 5 of degree 22
x ^ 22 + x ^ 2 + x + 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.
Primitive polynomial modulo 7 of degree 16
x ^ 16 + 2 x + 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.
Primitive polynomial modulo 17 of degree 14
x ^ 14 + x ^ 2 + 2 x + 6
 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.
Primitive polynomial modulo 137 of degree 7
x ^ 7 + x + 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.
Primitive polynomial modulo 223 of degree 8
x ^ 8 + x + 51
 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.
Primitive polynomial modulo 557 of degree 6
x ^ 6 + x + 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.
Factoring r = 15 into
3 5
Total number of primitive polynomials = 2. Begin testing...
Primitive polynomial modulo 2 of degree 4
x ^ 4 + x + 1
+ Statistics 

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

+
Confirming polynomial is primitive with an independent check.
Warning: You may wait an impossibly long time!
Polynomial is confirmed to be 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.
Factoring r = 121 into
11^2
Total number of primitive polynomials = 22. Begin testing...
Primitive polynomial modulo 3 of degree 5
x ^ 5 + 2 x + 1
+ Statistics 

 Total num. degree 5 polynomials mod 3 : 243
 Actually tested : 8
 Const. coeff. was primitive root : 3
 Free of linear factors : 1
 Irreducible or irred. to power : 1
 Had order r (x^r = integer) : 1
 Passed const. coeff. test : 1
 Had order m (x^m != integer) : 1

+
Confirming polynomial is primitive with an independent check.
Warning: You may wait an impossibly long time!
Polynomial is confirmed to be 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.
Total number of primitive polynomials = 6. Begin testing...
Primitive polynomial 1 of 6 modulo 2 of degree 5
x ^ 5 + x ^ 2 + 1
Primitive polynomial 2 of 6 modulo 2 of degree 5
x ^ 5 + x ^ 3 + 1
Primitive polynomial 3 of 6 modulo 2 of degree 5
x ^ 5 + x ^ 3 + x ^ 2 + x + 1
Primitive polynomial 4 of 6 modulo 2 of degree 5
x ^ 5 + x ^ 4 + x ^ 2 + x + 1
Primitive polynomial 5 of 6 modulo 2 of degree 5
x ^ 5 + x ^ 4 + x ^ 3 + x + 1
Primitive polynomial 6 of 6 modulo 2 of degree 5
x ^ 5 + x ^ 4 + x ^ 3 + x ^ 2 + 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.
ERROR: Expecting two arguments, p and n.
This program generates a primitive polynomial of degree n modulo p.
Usage: primpoly p n
Example: primpoly 2 4
generates the fourth degree polynomial
x ^ 4 + x + 1, whose coefficients use modulo 2 arithmetic.
Primitive polynomials find many uses in mathematics and communications
engineering:
* Generation of pseudonoise (PN) sequences for spread spectrum
communications and chip fault testing.
* Generation of CRC and Hamming codes.
* Generation of Galois (finite) fields for use in decoding ReedSolomon
and BCH error correcting codes.
Options:
pp c 2 4
does an addtional time consuming double check on the primitivity.
pp s 2 4
prints search statistics.
pp a 2 4
lists ALL primitive polynomials of degree 4 modulo 2.