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Old 2007-06-24, 15:20   #7
xilman
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"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

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Hmm, another example, N = 2131661909089739393111, gives somewhat better results:

Code:
Iterations       a_0   factor
        30         2  262533041
        99         3  262533041
        29         4  262533041
        43         5  262533041
       353         6  262533041
        72         7  262533041
        75         8  262533041
        34         9  262533041
        13        11  262533041
        23        12  262533041
       100        13  262533041
        25        14  262533041
        42        15  262533041
        41        16  262533041
        45        17  262533041
        51        18  262533041
       127        19  262533041
        35        20  262533041
       400        21  262533041
        49        22  262533041
        99        23  262533041
        38        24  262533041
       227        25  262533041
       161        26  262533041
        98        27  262533041
        56        28  262533041
       238        29  262533041
       225        30  262533041
        80        31  262533041
        27        32  262533041
       307        33  262533041
        18        34  262533041
        23        35  262533041
        67        36  262533041
        62        37  262533041
        22        38  262533041
        30        39  262533041
        60        40  262533041
        49        41  262533041
        85        42  262533041
        78        43  262533041
       266        44  262533041
        37        45  262533041
       101        46  262533041
       354        47  262533041
        72        48  262533041
        10        49  262533041
       148        50  262533041
        32        51  262533041
       107        52  262533041
         9        53  262533041
       317        54  262533041
        93        55  262533041
        99        56  262533041
       158        57  262533041
       227        58  8119594779271
        33        59  262533041
       170        60  262533041
        94        61  262533041
        40        62  262533041
       135        63  262533041
        53        64  262533041
        15        65  262533041
        33        66  262533041
        72        67  262533041
        56        68  262533041
       128        69  262533041
       111        70  262533041
        43        71  262533041
       337        72  262533041
        49        73  262533041
       238        74  262533041
        13        75  262533041
        97        76  262533041
       296        77  262533041
        67        78  262533041
       239        79  262533041
        30        80  262533041
       130        81  262533041
       288        82  262533041
        95        83  262533041
        73        84  262533041
        43        85  262533041
        31        86  262533041
       127        87  262533041
       317        88  262533041
        63        89  262533041
       134        90  262533041
        80        91  262533041
       161        92  262533041
        70        93  262533041
        93        94  262533041
       173        95  262533041
       520        96  262533041
        32        97  262533041
        83        98  262533041
       125        99  262533041
minimum = 9 maximum = 520 mean = 110.86 successes 97
sqrt(262533041) = 16202. There was only one failure to find the factor in 10,000 iterations and the successes were rather more impressive and the larger factor was found on one occasion.


Paul
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