GNFS Term Project

Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 54 upper bound on algebraic prime base (all first degree primes under): 108 upper bound on quadratic character prime base (all subsequent primes under): 227 search bounds for unit term: [ -181 , 181 ] found 25 simultaneously smooth pairs. found 33 simultaneously smooth pairs. found 60 simultaneously smooth pairs. found 65 simultaneously smooth pairs. 229 is a prime power, reducing to using ECM to factor 197 is a prime power, reducing to using ECM to factor 197 * 229 CPU time: 0.60 s, Wall time: 1.24 s Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 54 upper bound on algebraic prime base (all first degree primes under): 108 upper bound on quadratic character prime base (all subsequent primes under): 227 search bounds for unit term: [ -181 , 181 ] found 25 simultaneously smooth pairs. found 33 simultaneously smooth pairs. found 60 simultaneously smooth pairs. found 65 simultaneously smooth pairs. 229 is a prime power, reducing to using ECM to factor 197 is a prime power, reducing to using ECM to factor 197 * 229 CPU time: 0.60 s, Wall time: 1.24 s |

45113 45113 |

Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 58 upper bound on algebraic prime base (all first degree primes under): 116 upper bound on quadratic character prime base (all subsequent primes under): 244 search bounds for unit term: [ -400 , 400 ] found 34 simultaneously smooth pairs. found 45 simultaneously smooth pairs. found 82 simultaneously smooth pairs. failed to find a nontrivial factor. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 30 upper bound on algebraic prime base (all first degree primes under): 60 upper bound on quadratic character prime base (all subsequent primes under): 126 search bounds for unit term: [ -50 , 50 ] found 18 simultaneously smooth pairs. found 27 simultaneously smooth pairs. found 45 simultaneously smooth pairs. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 25 upper bound on algebraic prime base (all first degree primes under): 49 upper bound on quadratic character prime base (all subsequent primes under): 103 search bounds for unit term: [ -50 , 50 ] found 17 simultaneously smooth pairs. found 24 simultaneously smooth pairs. found 44 simultaneously smooth pairs. failed to find a nontrivial factor. failed to find a nontrivial factor. failed to find a nontrivial factor. 3 is a prime power, reducing to using ECM to factor 41 is a prime power, reducing to using ECM to factor 3 is a prime power, reducing to using ECM to factor 271 is a prime power, reducing to using ECM to factor 3^2 * 41 * 271 Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 58 upper bound on algebraic prime base (all first degree primes under): 116 upper bound on quadratic character prime base (all subsequent primes under): 244 search bounds for unit term: [ -400 , 400 ] found 34 simultaneously smooth pairs. found 45 simultaneously smooth pairs. found 82 simultaneously smooth pairs. failed to find a nontrivial factor. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 30 upper bound on algebraic prime base (all first degree primes under): 60 upper bound on quadratic character prime base (all subsequent primes under): 126 search bounds for unit term: [ -50 , 50 ] found 18 simultaneously smooth pairs. found 27 simultaneously smooth pairs. found 45 simultaneously smooth pairs. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 25 upper bound on algebraic prime base (all first degree primes under): 49 upper bound on quadratic character prime base (all subsequent primes under): 103 search bounds for unit term: [ -50 , 50 ] found 17 simultaneously smooth pairs. found 24 simultaneously smooth pairs. found 44 simultaneously smooth pairs. failed to find a nontrivial factor. failed to find a nontrivial factor. failed to find a nontrivial factor. 3 is a prime power, reducing to using ECM to factor 41 is a prime power, reducing to using ECM to factor 3 is a prime power, reducing to using ECM to factor 271 is a prime power, reducing to using ECM to factor 3^2 * 41 * 271 |

Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 68 upper bound on algebraic prime base (all first degree primes under): 136 upper bound on quadratic character prime base (all subsequent primes under): 286 search bounds for unit term: [ -3138 , 3138 ] found 29 simultaneously smooth pairs. found 68 simultaneously smooth pairs. found 83 simultaneously smooth pairs. found 123 simultaneously smooth pairs. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 44 upper bound on algebraic prime base (all first degree primes under): 88 upper bound on quadratic character prime base (all subsequent primes under): 185 search bounds for unit term: [ -50 , 50 ] found 20 simultaneously smooth pairs. found 47 simultaneously smooth pairs. found 58 simultaneously smooth pairs. 16 is a prime power, reducing to using ECM to factor Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 30 upper bound on algebraic prime base (all first degree primes under): 60 upper bound on quadratic character prime base (all subsequent primes under): 126 search bounds for unit term: [ -50 , 50 ] found 19 simultaneously smooth pairs. found 45 simultaneously smooth pairs. failed to find a nontrivial factor. 2 is a prime power, reducing to using ECM to factor 193 is a prime power, reducing to using ECM to factor 127 is a prime power, reducing to using ECM to factor 2^5 * 127 * 193 Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 68 upper bound on algebraic prime base (all first degree primes under): 136 upper bound on quadratic character prime base (all subsequent primes under): 286 search bounds for unit term: [ -3138 , 3138 ] found 29 simultaneously smooth pairs. found 68 simultaneously smooth pairs. found 83 simultaneously smooth pairs. found 123 simultaneously smooth pairs. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 44 upper bound on algebraic prime base (all first degree primes under): 88 upper bound on quadratic character prime base (all subsequent primes under): 185 search bounds for unit term: [ -50 , 50 ] found 20 simultaneously smooth pairs. found 47 simultaneously smooth pairs. found 58 simultaneously smooth pairs. 16 is a prime power, reducing to using ECM to factor Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 30 upper bound on algebraic prime base (all first degree primes under): 60 upper bound on quadratic character prime base (all subsequent primes under): 126 search bounds for unit term: [ -50 , 50 ] found 19 simultaneously smooth pairs. found 45 simultaneously smooth pairs. failed to find a nontrivial factor. 2 is a prime power, reducing to using ECM to factor 193 is a prime power, reducing to using ECM to factor 127 is a prime power, reducing to using ECM to factor 2^5 * 127 * 193 |

Factoring N = 606063 Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 67 upper bound on algebraic prime base (all first degree primes under): 134 upper bound on quadratic character prime base (all subsequent primes under): 282 search bounds for unit term: [ -2425 , 2425 ] found 31 simultaneously smooth pairs. found 43 simultaneously smooth pairs. found 85 simultaneously smooth pairs. 3 is a prime power, reducing to using ECM to factor 202021 is a prime power, reducing to using ECM to factor 3 * 202021 Test Case PASSED! True Factoring N = 606063 Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 67 upper bound on algebraic prime base (all first degree primes under): 134 upper bound on quadratic character prime base (all subsequent primes under): 282 search bounds for unit term: [ -2425 , 2425 ] found 31 simultaneously smooth pairs. found 43 simultaneously smooth pairs. found 85 simultaneously smooth pairs. 3 is a prime power, reducing to using ECM to factor 202021 is a prime power, reducing to using ECM to factor 3 * 202021 Test Case PASSED! True |

Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 68 upper bound on algebraic prime base (all first degree primes under): 136 upper bound on quadratic character prime base (all subsequent primes under): 136 search bounds for unit term: [ -3138 , 3138 ] found 48 simultaneously smooth pairs. found 101 simultaneously smooth pairs. The supposedly found square is not square! failed to find a square root in number field. failed to find squares. failed to find a nontrivial factor. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 42 upper bound on algebraic prime base (all first degree primes under): 84 upper bound on quadratic character prime base (all subsequent primes under): 84 search bounds for unit term: [ -50 , 50 ] found 40 simultaneously smooth pairs. The supposedly found square is not square! failed to find a square root in number field. failed to find squares. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 35 upper bound on algebraic prime base (all first degree primes under): 70 upper bound on quadratic character prime base (all subsequent primes under): 70 search bounds for unit term: [ -50 , 50 ] found 24 simultaneously smooth pairs. found 53 simultaneously smooth pairs. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 32 upper bound on algebraic prime base (all first degree primes under): 63 upper bound on quadratic character prime base (all subsequent primes under): 63 search bounds for unit term: [ -50 , 50 ] found 23 simultaneously smooth pairs. found 50 simultaneously smooth pairs. The supposedly found square is not square! failed to find a square root in number field. failed to find squares. 4 is a prime power, reducing to using ECM to factor 127 is a prime power, reducing to using ECM to factor 2 is a prime power, reducing to using ECM to factor 4 is a prime power, reducing to using ECM to factor 193 is a prime power, reducing to using ECM to factor 2^5 * 127 * 193 Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 68 upper bound on algebraic prime base (all first degree primes under): 136 upper bound on quadratic character prime base (all subsequent primes under): 136 search bounds for unit term: [ -3138 , 3138 ] found 48 simultaneously smooth pairs. found 101 simultaneously smooth pairs. The supposedly found square is not square! failed to find a square root in number field. failed to find squares. failed to find a nontrivial factor. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 42 upper bound on algebraic prime base (all first degree primes under): 84 upper bound on quadratic character prime base (all subsequent primes under): 84 search bounds for unit term: [ -50 , 50 ] found 40 simultaneously smooth pairs. The supposedly found square is not square! failed to find a square root in number field. failed to find squares. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 35 upper bound on algebraic prime base (all first degree primes under): 70 upper bound on quadratic character prime base (all subsequent primes under): 70 search bounds for unit term: [ -50 , 50 ] found 24 simultaneously smooth pairs. found 53 simultaneously smooth pairs. Parameter Selection for GNFS: upper bound on rational prime base (all primes under): 32 upper bound on algebraic prime base (all first degree primes under): 63 upper bound on quadratic character prime base (all subsequent primes under): 63 search bounds for unit term: [ -50 , 50 ] found 23 simultaneously smooth pairs. found 50 simultaneously smooth pairs. The supposedly found square is not square! failed to find a square root in number field. failed to find squares. 4 is a prime power, reducing to using ECM to factor 127 is a prime power, reducing to using ECM to factor 2 is a prime power, reducing to using ECM to factor 4 is a prime power, reducing to using ECM to factor 193 is a prime power, reducing to using ECM to factor 2^5 * 127 * 193 |