which speed conserve fuel the most？

[cosmo kramer]

CI = 0 corresponds to minimum fuel consumption (max range)

What a mix up of terms.

Fuel consumption is measured in amount pr. time unit (kg pr. hour). Hence, "minimum fuel consumption" would occur at the speed where the least kg pr. time unit occurs. This is according to all international definitions Max Endurance, not Max Range. For most jets, that would be slightly above clean speed (Les Green dôt spéed?).

It seems either Airbus has no idea of basic concepts (hope not) or that something go screwed up the translation from French. Perhaps it originally read:
"CI = 0 correspond to minimum (trip) fuel consumed (max range)".

At least, then it would make sense. I am sure they mean it all well, though. Alors! Eh bien..

So to reiterate if the original poster wants:

1. Longest time in the air:
   Holding speed from the FMC (Boeing)
2. Lowest trip fuel:
   ECON cruise CI =0 with forecasted wind in the legs page (*)

(*) Strike the previous comment about LRC being a better choice for the Classic (although wind corrected):

Boeing: AERO - Fuel Conservation Strategies
If faced with a low fuel situation at destination, many pilots will opt to fly LRC speed thinking that it will give them the most miles from their remaining fuel. As shown in figure 2, the best strategy to conserve fuel is to select a very low cost index, with zero providing the maximum range.