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cat unitTest.log 

Primpoly Version 16.4 - A Program for Computing Primitive Polynomials.
Copyright (C) 1999-2026 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.

Begin unit testing...
TEST:  Parsing the command line options..........PASS!
TEST:  parsing constant 0.........PASS!
TEST:  parsing polynomial and modulus:  2 x ^ 3 + 3 x + 4, 5.........PASS!
TEST:  parsing polynomial, modulus:  2x, 7..........PASS!
TEST:  parsing constant 2.........PASS!
TEST:  parsing bad syntax:  x + 1.........PASS!
TEST:  Switching from base 2147483648 to new base 10.........PASS!
TEST:  BigInt() default constructor..........PASS!
TEST:  BigInt( 0 ) constructor from zero..........PASS!
TEST:  BigInt( 1234 ) constructor from uint.........PASS!
TEST:  BigInt u( "1234" ) constructor from <decimal number string>.........PASS!
TEST:  BigInt u( "12x34" ) constructor from invalid <decimal number string>.........PASS!
TEST:  BigInt copy constructor: u( 123 ) ; v( u )..........PASS!
TEST:  BigInt u = v assignment for BigInt.........PASS!
TEST:  cast BigInt to uint implicitly Bigint u ; uint d = u..........PASS!
TEST:  cast BigInt to uint explicitly: BigInt u ; static_cast<uint>(u)..........PASS!
TEST:  overflow during cast from BigInt to uint?.........PASS!
TEST:  stream output << BigInt.........PASS!
TEST:  stream input >> BigInt.........PASS!
TEST:  BigInt == uint.........PASS!
TEST:  BigInt == BigInt.........PASS!
TEST:  BigInt > uint.........PASS!
TEST:  BigInt -= uint.........PASS!
TEST:  BigInt -= uint underflow.........PASS!
TEST:  BigInt += uint.........PASS!
TEST:  BigInt *= uint.........PASS!
TEST:  BigInt /= uint.........PASS!
TEST:  BigInt /= uint underflow to zero..........PASS!
TEST:  ++BigInt.........PASS!
TEST:  --BigInt.........PASS!
TEST:  BigInt++.........PASS!
TEST:  BigInt--.........PASS!
TEST:  one digit BigInt + uint.........PASS!
TEST:  two digit BigInt + uint.........PASS!
TEST:  BigInt + BigInt.........PASS!
TEST:  BigInt + BigInt.........PASS!
TEST:  BigInt - BigInt.........PASS!
TEST:  BigInt - BigInt < 0.........PASS!
TEST:  BigInt - uint.........PASS!
TEST:  one digit BigInt * BigInt.........PASS!
TEST:  two digit BigInt * BigInt.........PASS!
TEST:  BigInt multidigit *.........PASS!
TEST:  BigInt multidigit *=.........PASS!
TEST:  BigInt / BigInt one digit divisor..........PASS!
TEST:  BigInt / BigInt multidigit.........PASS!
TEST:  BigInt / BigInt leading zero digit..........PASS!
TEST:  BigInt / 0 .........PASS!
TEST:  BigInt % BigInt with u > v.........PASS!
TEST:  BigInt multidigit mod with normalizing constant d = 1.........PASS!
TEST:  BigInt % BigInt with u < v.........PASS!
TEST:  BigInt % uint = 314159 / 9 = 5 with uint < base .........PASS!
TEST:  BigInt % uint = 398765 % 3457u with uint > base overflow?.........PASS!
TEST:  BigInt / BigInt low probability if branch..........PASS!
TEST:  Switching back from base 10 to oldBase 2147483648.........PASS!
TEST:  Decimal string to BigInt conversion and back to decimal string using default base..........PASS!
TEST:  BigInt z = x * y then x =? z / y multidigit with default base..........PASS!
TEST:  BigInt testBit.........PASS!
TEST:  testBit().........PASS!
TEST:  BigInt power( uint 2, uint 100 ).........PASS!
TEST:  BigInt ceilLg( 6 ).........PASS!
TEST:  ModP 10 = 3 (mod 7).........PASS!
TEST:  ModP -10 = 4 (mod 7).........PASS!
TEST:  uint gcd( 85, 25 ) = 5.........PASS!
TEST:  BigInt gcd( 779953197883173551166308319545, 1282866356929526866866376009397 ) = 1.........PASS!
TEST:  PowerMod uint 3^10 = 4 (mod 7).........PASS!
TEST:  PowerMod BigInt 3^10 = 4 (mod 7).........PASS!
TEST:  PowerMod with out of range inputs..........PASS!
TEST:  InverseModP 3 * 5 = 1 (mod 7).........PASS!
TEST:  IsPrimitiveRoot.   3 is a primitive root of 7..........PASS!
TEST:  IsPrimitiveRoot.   2 is a primitive root of 11..........PASS!
TEST:  IsPrimitiveRoot.   3 is NOT a primitive root of 11..........PASS!
TEST:  IsPrimitiveRoot.   5 is a primitive root of 65003..........PASS!
TEST:  IsPrimitiveRoot.   8 is NOT a primitive root of 65003..........PASS!
TEST:  constant coefficient test..........PASS!
TEST:  constant coefficient is primitive root..........PASS!
TEST:  isProbablyPrime uint 97 with random x = 10 says yes..........PASS!
TEST:  isAlmostSurelyPrime 97 says yes..........PASS!
TEST:  isAlmostSurelyPrime BigInt 97 says yes.........PASS!
TEST:  isAlmostSurelyPrime 49 says no..........PASS!
TEST:  isAlmostSurelyPrime on the 10000th prime number 104729 which is >> 32768 = 2^(32/2-1) says yes..........PASS!
TEST:  Trial division factoring on unsigned int..........PASS!
TEST:  Trial division factor BigInt 337500 = 2^2 3^3 5^5..........PASS!
TEST:  Pollard Rho factor unsigned int 25852 = 2^2 23 281.........PASS!
TEST:  Pollard Rho factor BigInt 25852 = 2^2 23 281.........PASS!
TEST:  Factor Copy constructor.........PASS!
TEST:  Factor assignment operator.........PASS!
TEST:  Factor BigInt 24018350267611933650627567399079537500 = 2^2 3^3 5^5 7^7 11^11 13^13..........PASS!
TEST:  BigInt computation of p^n, r, factors of r, EulerPhi[ p^n - 1]/n for p = 2.........PASS!
TEST:  BigInt computation of p^n, r, factors of r, EulerPhi[ p^n - 1]/n for p > 2
	ERROR:  BigInt computation of p^n, r, factors of r, EulerPhi[ p^n - 1]/n for p > 2
	ERROR:  BigIntMathError:  BigInt::operator-=  negative result for u - v = 0 - 1 at ../SourceCode/Primpoly/ppBigInt.cpp: line 1057

TEST:  Factor tables for Factor<uint>.........PASS!
TEST:  Factor tables for Factor<BigInt>.........PASS!
TEST:  Polynomial() default constructor..........PASS!
TEST:  Polynomial() from string..........PASS!
TEST:  Polynomial = string..........PASS!
TEST:  Polynomial() from string with negative constant..........PASS!
TEST:  Polynomial() to string..........PASS!
TEST:  Polynomial() copy constructor..........PASS!
TEST:  Polynomial assignment operator..........PASS!
TEST:  Polynomial()[] read only operator..........PASS!
TEST:  Polynomial()[] accessing coeff higher than its degree..........PASS!
TEST:  Polynomial()[] lvalue operator..........PASS!
TEST:  Polynomial() += operator..........PASS!
TEST:  Polynomial() += operator..........PASS!
TEST:  Polynomial() + operator..........PASS!
TEST:  Polynomial * scalar.........PASS!
TEST:  Polynomial evaluation x^4 + 3x + 3 (mod 5).........PASS!
TEST:  Polynomial evaluation x^4 + x + 1 (mod 2).........PASS!
TEST:  Polynomial hasLinearFactor is true.........PASS!
TEST:  Polynomial hasLinearFactor is false.........PASS!
TEST:  Polynomial isInteger.........PASS!.........PASS!
TEST:  Polynomial initial and next trial polynomials.........PASS!
TEST:  PolyMod constructor from polynomials..........PASS!
TEST:  PolyMod constructor from string and polynomial..........PASS!
TEST:  PolyMod timesX..........PASS!
TEST:  PolyMod autoconvolve..........PASS!
TEST:  PolyMod convolve..........PASS!
TEST:  PolyMod coeffOfSquare..........PASS!
TEST:  PolyMod coeffOfProduct..........PASS!
TEST:  PolyMod square..........PASS!
TEST:  PolyMod operator* and implicitly, operator*=.........PASS!
TEST:  PolyMod x_to_power and isInteger().........PASS!
TEST:  PolyOrder reduced Q-I matrix
	ERROR:  PolynomialRangeError error:  PolyOrder: problem computing p^n or r = (p^n - 1 )/ (p - 1), or factoring r, or finding EulerPhi( p^n - 1 )/ n  p = 5 n = 4 at ../SourceCode/Primpoly/ppPolynomial.cpp: line 2638BigInt::operator-=  negative result for u - v = 0 - 1 at ../SourceCode/Primpoly/ppBigInt.cpp: line 1057

TEST:  PolyOrder 3 distinct factors out of 4
	ERROR:  PolynomialRangeError error:  PolyOrder: problem computing p^n or r = (p^n - 1 )/ (p - 1), or factoring r, or finding EulerPhi( p^n - 1 )/ n  p = 5 n = 4 at ../SourceCode/Primpoly/ppPolynomial.cpp: line 2638BigInt::operator-=  negative result for u - v = 0 - 1 at ../SourceCode/Primpoly/ppBigInt.cpp: line 1057

TEST:  PolyOrder 2 distinct factors.........PASS!
TEST:  PolyOrder irreducible
	ERROR:  PolynomialRangeError error:  PolyOrder: problem computing p^n or r = (p^n - 1 )/ (p - 1), or factoring r, or finding EulerPhi( p^n - 1 )/ n  p = 5 n = 4 at ../SourceCode/Primpoly/ppPolynomial.cpp: line 2638BigInt::operator-=  negative result for u - v = 0 - 1 at ../SourceCode/Primpoly/ppBigInt.cpp: line 1057

TEST:  PolyOrder 1 distinct factor 4 times
	ERROR:  PolynomialRangeError:  PolyOrder: problem computing p^n or r = (p^n - 1 )/ (p - 1), or factoring r, or finding EulerPhi( p^n - 1 )/ n  p = 5 n = 4 at ../SourceCode/Primpoly/ppPolynomial.cpp: line 2638BigInt::operator-=  negative result for u - v = 0 - 1 at ../SourceCode/Primpoly/ppBigInt.cpp: line 1057

End unit testing...
SORRY.  One or more unit tests failed!




$ gdb Bin/Primpoly.exe

GNU gdb 6.3.50-20050815 (Apple version gdb-1510) (Wed Sep 22 02:45:02 UTC 2010)
Copyright 2004 Free Software Foundation, Inc.
GDB is free software, covered by the GNU General Public License, and you are
welcome to change it and/or distribute copies of it under certain conditions.
Type "show copying" to see the conditions.
There is absolutely no warranty for GDB.  Type "show warranty" for details.
This GDB was configured as "x86_64-apple-darwin"...Reading symbols for shared libraries ... done

(gdb) b ppBigInt.cpp:1057
Breakpoint 1 at 0x10000d5f7: file ../SourceCode/Primpoly/ppBigInt.cpp, line 1057.

(gdb) run 2 4
Starting program: /Volumes/Sean/Sean/WebSite/Mathematics/AbstractAlgebra/PrimitivePolynomials/Project/Build/Bin/Primpoly.exe 2 4
Reading symbols for shared libraries ++. done

Primpoly Version 16.4 - A Program for Computing Primitive Polynomials.
Copyright (C) 1999-2026 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.

Pollard rho n = 25852 c = 2
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 25852 k = 1 l = 1
    after division, n_ = 25852 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 25852 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 12926 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 12926 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 6463 x = 27 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 22 n_ = 6463 k = 2 l = 2
    after division, n_ = 6463 x = 731 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 726 n_ = 6463 k = 1 l = 2
    after division, n_ = 6463 x = 4397 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 3666 n_ = 6463 k = 4 l = 4
    after division, n_ = 6463 x = 2778 xp = 731
    inner while loop, gcd = g = 23 |x -xp| = 2047 n_ = 6463 k = 3 l = 4
    >>>>>prime factor g = 23
    after division, n_ = 281 x = 249 xp = 169
    >>>>>prime factor n_ = 281
Pollard rho n = 25852 c = 2
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 25852 k = 1 l = 1
    after division, n_ = 25852 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 25852 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 12926 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 12926 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 6463 x = 27 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 22 n_ = 6463 k = 2 l = 2
    after division, n_ = 6463 x = 731 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 726 n_ = 6463 k = 1 l = 2
    after division, n_ = 6463 x = 4397 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 3666 n_ = 6463 k = 4 l = 4
    after division, n_ = 6463 x = 2778 xp = 731
    inner while loop, gcd = g = 23 |x -xp| = 2047 n_ = 6463 k = 3 l = 4
    >>>>>prime factor g = 23
    after division, n_ = 281 x = 249 xp = 169
    >>>>>prime factor n_ = 281
Pollard rho n = 24018350267611933650627567399079537500 c = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 24018350267611933650627567399079537500 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 8006116755870644550209189133026512500 x = 5 xp = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 8006116755870644550209189133026512500 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 2668705585290214850069729711008837500 x = 5 xp = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 2668705585290214850069729711008837500 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 889568528430071616689909903669612500 x = 5 xp = 2
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 889568528430071616689909903669612500 k = 1 l = 1
    after division, n_ = 889568528430071616689909903669612500 x = 27 xp = 5
    inner while loop, gcd = g = 22 |x -xp| = 22 n_ = 889568528430071616689909903669612500 k = 2 l = 2
    g = 22 isn't prime 
Pollard rho n = 889568528430071616689909903669612500 c = 5
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 889568528430071616689909903669612500 k = 1 l = 1
    after division, n_ = 889568528430071616689909903669612500 x = 30 xp = 5
    inner while loop, gcd = g = 25 |x -xp| = 25 n_ = 889568528430071616689909903669612500 k = 2 l = 2
    g = 25 isn't prime 
Pollard rho n = 68719476735 c = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 68719476735 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 22906492245 x = 5 xp = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 22906492245 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 7635497415 x = 5 xp = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 7635497415 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 2545165805 x = 5 xp = 2
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 2545165805 k = 1 l = 1
    after division, n_ = 2545165805 x = 27 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 22 n_ = 2545165805 k = 2 l = 2
    after division, n_ = 2545165805 x = 731 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 726 n_ = 2545165805 k = 1 l = 2
    after division, n_ = 2545165805 x = 534363 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 533632 n_ = 2545165805 k = 4 l = 4
    after division, n_ = 2545165805 x = 485245611 xp = 731
    inner while loop, gcd = g = 5 |x -xp| = 485244880 n_ = 2545165805 k = 3 l = 4
    >>>>>prime factor g = 5
    after division, n_ = 509033161 x = 485245611 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 485244880 n_ = 509033161 k = 3 l = 4
    after division, n_ = 509033161 x = 164836970 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 164836239 n_ = 509033161 k = 2 l = 4
    after division, n_ = 509033161 x = 144374675 xp = 731
    inner while loop, gcd = g = 13 |x -xp| = 144373944 n_ = 509033161 k = 1 l = 4
    >>>>>prime factor g = 13
    after division, n_ = 39156397 x = 26905484 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 26904753 n_ = 39156397 k = 1 l = 4
    after division, n_ = 39156397 x = 5044848 xp = 26905484
    inner while loop, gcd = g = 259 |x -xp| = 21860636 n_ = 39156397 k = 8 l = 8
    g = 259 isn't prime 
Pollard rho n = 39156397 c = 5
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 39156397 k = 1 l = 1
    after division, n_ = 39156397 x = 30 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 25 n_ = 39156397 k = 2 l = 2
    after division, n_ = 39156397 x = 905 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 900 n_ = 39156397 k = 1 l = 2
    after division, n_ = 39156397 x = 819030 xp = 905
    inner while loop, gcd = g = 7 |x -xp| = 818125 n_ = 39156397 k = 4 l = 4
    >>>>>prime factor g = 7
    after division, n_ = 5593771 x = 819030 xp = 905
    inner while loop, gcd = g = 1 |x -xp| = 818125 n_ = 5593771 k = 4 l = 4
    after division, n_ = 5593771 x = 5122585 xp = 905
    inner while loop, gcd = g = 73 |x -xp| = 5121680 n_ = 5593771 k = 3 l = 4
    >>>>>prime factor g = 73
    after division, n_ = 76627 x = 65203 xp = 905
    inner while loop, gcd = g = 1 |x -xp| = 64298 n_ = 76627 k = 3 l = 4
    after division, n_ = 76627 x = 12000 xp = 905
    inner while loop, gcd = g = 1 |x -xp| = 11095 n_ = 76627 k = 2 l = 4
    after division, n_ = 76627 x = 17872 xp = 905
    inner while loop, gcd = g = 19 |x -xp| = 16967 n_ = 76627 k = 1 l = 4
    >>>>>prime factor g = 19
    after division, n_ = 4033 x = 1740 xp = 905
    inner while loop, gcd = g = 1 |x -xp| = 835 n_ = 4033 k = 1 l = 4
    after division, n_ = 4033 x = 2855 xp = 1740
    inner while loop, gcd = g = 1 |x -xp| = 1115 n_ = 4033 k = 8 l = 8
    after division, n_ = 4033 x = 337 xp = 1740
    inner while loop, gcd = g = 1 |x -xp| = 1403 n_ = 4033 k = 7 l = 8
    after division, n_ = 4033 x = 650 xp = 1740
    inner while loop, gcd = g = 109 |x -xp| = 1090 n_ = 4033 k = 6 l = 8
    >>>>>prime factor g = 109
    after division, n_ = 37 x = 21 xp = 1
    >>>>>prime factor n_ = 37
p = 2
n = 36
p^n = 68719476736
r = (p^n-1)/(p-1) = 68719476735
8 sorted unique factors of r
3 ^ 3
5 ^ 1
7 ^ 1
13 ^ 1
19 ^ 1
37 ^ 1
73 ^ 1
109 ^ 1
8 distinct primes for p^n - 1
3
5
7
13
19
37
73
109
numPrimitivePoly = 725594112
Pollard rho n = 435984840 c = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 435984840 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 145328280 x = 5 xp = 2
    inner while loop, gcd = g = 3 |x -xp| = 3 n_ = 145328280 k = 1 l = 1
    >>>>>prime factor g = 3
    after division, n_ = 48442760 x = 5 xp = 2
    inner while loop, gcd = g = 1 |x -xp| = 3 n_ = 48442760 k = 1 l = 1
    after division, n_ = 48442760 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 48442760 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 24221380 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 24221380 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 12110690 x = 27 xp = 5
    inner while loop, gcd = g = 2 |x -xp| = 22 n_ = 12110690 k = 2 l = 2
    >>>>>prime factor g = 2
    after division, n_ = 6055345 x = 27 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 22 n_ = 6055345 k = 2 l = 2
    after division, n_ = 6055345 x = 731 xp = 5
    inner while loop, gcd = g = 1 |x -xp| = 726 n_ = 6055345 k = 1 l = 2
    after division, n_ = 6055345 x = 534363 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 533632 n_ = 6055345 k = 4 l = 4
    after division, n_ = 6055345 x = 4022296 xp = 731
    inner while loop, gcd = g = 5 |x -xp| = 4021565 n_ = 6055345 k = 3 l = 4
    >>>>>prime factor g = 5
    after division, n_ = 1211069 x = 389089 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 388358 n_ = 1211069 k = 3 l = 4
    after division, n_ = 1211069 x = 569578 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 568847 n_ = 1211069 k = 2 l = 4
    after division, n_ = 1211069 x = 356504 xp = 731
    inner while loop, gcd = g = 1 |x -xp| = 355773 n_ = 1211069 k = 1 l = 4
    after division, n_ = 1211069 x = 676882 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 320378 n_ = 1211069 k = 8 l = 8
    after division, n_ = 1211069 x = 39984 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 316520 n_ = 1211069 k = 7 l = 8
    after division, n_ = 1211069 x = 109178 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 247326 n_ = 1211069 k = 6 l = 8
    after division, n_ = 1211069 x = 494588 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 138084 n_ = 1211069 k = 5 l = 8
    after division, n_ = 1211069 x = 728850 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 372346 n_ = 1211069 k = 4 l = 8
    after division, n_ = 1211069 x = 227411 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 129093 n_ = 1211069 k = 3 l = 8
    after division, n_ = 1211069 x = 694485 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 337981 n_ = 1211069 k = 2 l = 8
    after division, n_ = 1211069 x = 1185977 xp = 356504
    inner while loop, gcd = g = 1 |x -xp| = 829473 n_ = 1211069 k = 1 l = 8
    after division, n_ = 1211069 x = 1063655 xp = 1185977
    inner while loop, gcd = g = 29 |x -xp| = 122322 n_ = 1211069 k = 16 l = 16
    >>>>>prime factor g = 29
    after division, n_ = 41761 x = 19630 xp = 16669
    >>>>>prime factor n_ = 41761
p = 17
n = 8
p^n = 6975757441
r = (p^n-1)/(p-1) = 435984840
5 sorted unique factors of r
2 ^ 3
3 ^ 2
5 ^ 1
29 ^ 1
41761 ^ 1
1 sorted unique factors of p-1
2 ^ 4




Breakpoint 1, BigInt::operator-= (this=0x7fff5fbf9170, v=@0x7fff5fbf95b0) at ../SourceCode/Primpoly/ppBigInt.cpp:1057
1057	           << " at " << __FILE__ << ": line " << __LINE__ ;

(gdb) up
#1  0x000000010000d8f3 in operator- (u=@0x1002036d8, v=@0x7fff5fbf95b0) at ../SourceCode/Primpoly/ppBigInt.cpp:976
976	    return BigInt( u ) -= v ;

(gdb) up
#2  0x0000000100047527 in factorRAndFindNumberOfPrimitivePolynomials (p=17, n=8, maxNumPossiblePoly=@0x7fff5fbfbcf0, r=@0x7fff5fbfb9f0, factorsOfR=@0x7fff5fbfaea0, numPrimitivePoly=@0x7fff5fbfbde0) at ../SourceCode/Primpoly/ppFactor.cpp:2513
2513	        numPrimitivePoly *= (allDistinctPrimes[ i ] - static_cast<BigInt>( 1u )) ;

(gdb) l
2508	    //               i
2509	    // Multiply by -------
2510	    //               p
2511	    //                i
2512	    for (unsigned int i = 0u ;  i < allDistinctPrimes.size() ; ++i)
2513	        numPrimitivePoly *= (allDistinctPrimes[ i ] - static_cast<BigInt>( 1u )) ;
2514	
2515	    for (unsigned int i = 0u ;  i < allDistinctPrimes.size() ; ++i)
2516	        numPrimitivePoly /=  allDistinctPrimes[ i ] ;
2517	

(gdb) p p
$1 = 17

(gdb) p n
$2 = 8

(gdb) call printNumber(std::cout,r)            
 BigInt number 435984840  (base b = 2147483648, number of digits = 1)

(gdb) call printNumber(std::cout,maxNumPossiblePoly)
 BigInt number 3 533306497  (base b = 2147483648, number of digits = 2)

(gdb) p factorsOfR.num()
$3 = 5

(gdb) call printNumber(std::cout,allDistinctPrimes[i])
 BigInt number 0  (base b = 2147483648, number of digits = 1)

(gdb) p i
$1 = 5

(gdb) p allDistinctPrimes.size()
$2 = 6

(gdb) call printNumber(std::cout,allDistinctPrimes[0])
 BigInt number 2  (base b = 2147483648, number of digits = 1)
(gdb) call printNumber(std::cout,allDistinctPrimes[1])
 BigInt number 3  (base b = 2147483648, number of digits = 1)
(gdb) call printNumber(std::cout,allDistinctPrimes[2])
 BigInt number 5  (base b = 2147483648, number of digits = 1)
(gdb) call printNumber(std::cout,allDistinctPrimes[3])
 BigInt number 29  (base b = 2147483648, number of digits = 1)
(gdb) call printNumber(std::cout,allDistinctPrimes[4])
 BigInt number 41761  (base b = 2147483648, number of digits = 1)
(gdb) call printNumber(std::cout,allDistinctPrimes[5])
 BigInt number 0  (base b = 2147483648, number of digits = 1)
(gdb) q
The program is running.  Exit anyway? (y or n) y