Here are a few examples and test cases which show the program output on various inputs. I omit printing the legal notice after the first example. I turn off the independent check that the polynomial is primitive after the first few runs, because it would take too long to finish (it's used for debugging.)
primpoly 138 3
Primpoly Version 5.3 - A Program for Computing Primitive Polynomials. Copyright (C) 1999-2008 by Sean Erik O'Connor. All Rights Reserved.
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.
p must be a prime number.
$ primpoly -sc 2 4
Factoring r = 15 into
3 5
Total number of primitive polynomials = 2. Begin testing...
aabcdef
Primitive polynomial modulo 2 of degree 4
x ^ 4 + x + 1
+--------- Statistics ----------------------------
|
| Total num. degree 4 polynomials mod 2 : 16
|
| Actually tested : 4
| a. Const. coeff. was primitive root : 2
| b. Free of linear factors : 1
| c. Irreducible or irred. to power : 1
| d. Had order r (x^r = integer) : 1
| e. Passed const. coeff. test : 1
| f. 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.
$ primpoly -s 5 5
Factoring r = 781 into
11 71
Total number of primitive polynomials = 280. Begin testing...
aaaaaaaaabcdef
Primitive polynomial modulo 5 of degree 5
x ^ 5 + 4 x + 2
+--------- Statistics ----------------------------
|
| Total num. degree 5 polynomials mod 5 : 3125
|
| Actually tested : 23
| a. Const. coeff. was primitive root : 9
| b. Free of linear factors : 1
| c. Irreducible or irred. to power : 1
| d. Had order r (x^r = integer) : 1
| e. Passed const. coeff. test : 1
| f. Had order m (x^m != integer) : 1
|
+-------------------------------------------------
$ primpoly -s 2 55
Factoring r = 36028797018963967 into
23 31 89 881 3191 201961
Total number of primitive polynomials = 598690870272000. Begin testing...
aababaabaaababaaabaababaabaaabaababaaababaabaaababaaabcdef
Primitive polynomial modulo 2 of degree 55
x ^ 55 + x ^ 6 + x ^ 2 + x + 1
+--------- Statistics ----------------------------
|
| Total num. degree 55 polynomials mod 2 : 36028797018963968
|
| Actually tested : 72
| a. Const. coeff. was primitive root : 36
| b. Free of linear factors : 18
| c. Irreducible or irred. to power : 1
| d. Had order r (x^r = integer) : 1
| e. Passed const. coeff. test : 1
| f. Had order m (x^m != integer) : 1
|
+-------------------------------------------------
$ primpoly 137 10 ERROR: p to the nth power must be smaller than 4294967295
$ primpoly -s 137 8
Factoring r = 912484779174120 into
2^3 3 5 23 41 1409 1877 3049
Total number of primitive polynomials = 3627463779287040. Begin testing...
abcdeabcdeabcdeababcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcde
abcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabc
deabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcde
abcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabc
deabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdef
Primitive polynomial modulo 137 of degree 8
x ^ 8 + x + 3
+--------- Statistics ----------------------------
|
| Total num. degree 8 polynomials mod 137 : 124097929967680321
|
| Actually tested : 141
| a. Const. coeff. was primitive root : 66
| b. Free of linear factors : 66
| c. Irreducible or irred. to power : 65
| d. Had order r (x^r = integer) : 65
| e. Passed const. coeff. test : 65
| f. Had order m (x^m != integer) : 1
|
+-------------------------------------------------
primpoly -a 2 5 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
