ECM is a probabilistic algorithm. Its probability of success depends on the size of the (usually unknown) factor p to be found, on the step 1 and 2 bounds B1 and B2, and possibly on some other implementation-dependent parameters.

The table below indicates for each factor size what is the optimal step 1 limit B1 to use (first argument of the GMP-ECM program). The column "expected curves" corresponds to the default parameters of GMP-ECM. Those figures can be reproduced using thedigits | optimal B1 | expected curves (default parameters for GMP-ECM 6) |
expected curves (default parameters for GMP-ECM 7) |

20 | 11,000 | 86 | 107 |

25 | 50,000 | 214 | 261 |

30 | 250,000 | 430 | 513 |

35 | 1,000,000 | 910 | 1,071 |

40 | 3,000,000 | 2,351 | 2,753 |

45 | 11,000,000 | 4,482 | 5,208 |

50 | 43,000,000 | 7,557 | 8,704 |

55 | 110,000,000 | 17,884 | 20,479 |

60 | 260,000,000 | 42,057 | 47,888 |

65 | 850,000,000 | 69,471 | 78,923 |

70 | 2,900,000,000 | 102,212 | 115,153 |

75 | 7,600,000,000 | 188,056 | 211,681 |

80 | 25,000,000,000 | 265,557 | 296,479 |

Update June 5, 2019: Pierrick Gaudry computed experimentally optimal
parameters with GMP-ECM 7 (using the output of `ecm -v`) for a
512-bit input, and for factor size from 30 to 225 bits, by steps of 5 bits.
The optimal B1 values he found below follow a regression of the form
log(B1) = a*bits+b, with a = 0.0750 and b = 5.332.
and the corresponding total effort (B1 times number of curves) follows
a regression of the form log(B1*ncurves) = d*bits^{2}+e*bits+f,
with d = -0.000203, e = 0.177 and f = 3.097.
In terms of the number of curves, one seems to have
B1 = 150*ncurves^{1.5}.
This table, where the B1 values grow more quickly than in the above one,
should be considered as more accurate. The above table is kept for
reference.

bits | optimal B1 | expected curves |

30 | 1358 | 2 |

35 | 1270 | 5 |

40 | 1629 | 10 |

45 | 4537 | 10 |

50 | 12322 | 9 |

55 | 12820 | 18 |

60 | 21905 | 21 |

65 | 24433 | 41 |

70 | 32918 | 66 |

75 | 64703 | 71 |

80 | 76620 | 119 |

85 | 155247 | 123 |

90 | 183849 | 219 |

95 | 245335 | 321 |

100 | 445657 | 339 |

105 | 643986 | 468 |

110 | 1305195 | 439 |

115 | 1305195 | 818 |

120 | 3071166 | 649 |

125 | 3784867 | 949 |

130 | 4572523 | 1507 |

135 | 7982718 | 1497 |

140 | 9267681 | 2399 |

145 | 22025673 | 1826 |

150 | 22025673 | 3159 |

155 | 26345943 | 4532 |

160 | 35158748 | 6076 |

165 | 46919468 | 8177 |

170 | 47862548 | 14038 |

175 | 153319098 | 7166 |

180 | 153319098 | 12017 |

185 | 188949210 | 16238 |

190 | 410593604 | 13174 |

195 | 496041799 | 17798 |

200 | 491130495 | 29584 |

205 | 1067244762 | 23626 |

210 | 1056677983 | 38609 |

215 | 1328416470 | 49784 |

220 | 1315263832 | 81950 |

225 | 2858117139 | 63461 |