Most energy efficient way to power up LED 3528

Thanks for the answer!

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First, some clarification about Your post.

With a single, 3.7V battery, you must connect the LEDs in parallel with a current limit resistor on each one.

I don't understand what the resistor do, and why is it important to put in the circuit.

I'd look into putting them all in series and using a boosting converter

Sorry for this stupid question, but what is a boosting converter, and more important why I need one in my circuit?

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Because of the large voltage swing of lithium cell (you are using lithium?), a series resistor isn't
going to give constant current, the cell voltage drops from 4.2V to 3.5 or so, so a series resistor will
mean the current drops as the battery discharges

I'm going to use a TP, is enough?

And now I will try to explain better.

My goal is to power on a lamp of about 20 lumens for 5/6 hours. The lithium battery that I'm going to use (I don't know the voltage, 3.7 is good?. The mAh I'm thinking are about 500/600, always for achieving the 5/6 hours) it will be connected to a TP, that will be connected to a solar panel (what is the minimum voltage that is needed for recharging the battery?). With a physical switch, I power on or off the circuit with the LEDs, connected to the load pin of the TP board (no problem, I know that I can't recharge if there is some load, by I'm going to use during the night). Space is small, so no big battery and big panel, think that I must store everything in a 9-10cm diameter circle. Also, the solar panel must completely charge the battery. So, how can I reach the most energy saver but bright lamp?

Thanks to all!

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