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