[attachment=26504]
http://xcraft.net/battle/index.php?battle_id=1b60be72972b218e3b68e38cc47a4a7f
4000 providers and still a moon formed

Can you explain where's problem?

how many providers or harvesters are required to stop a moon forming?

It takes time to recycle the debris, and moon formation is determined at the end of the battle. In this case, it looks like the fight lasted for 10 minutes and produced a total of 13M metal + 8M mineral.

At the end of the battle (10 minutes), your providers had collected about 6M metal and about 5M minerals, leaving roughly 7M metal and 3M mineral....however, that still left enough to form a moon when the battle ended, and it seems that is exactly what happened.

In order to prevent a moon from forming, there must not be enough debris when the fight actually ends...either more providers, higher recycling speed, or extend the fight to allow providers to collect more debris would have been options to prevent moon formation

ok so it is not that they prevent the moon but just recycle enough debris that there is not enough left for a moon! so the biger the battle the more needed

Yes, and the bigger the debris field, the more recyclers/time of recycling needed to prevent a moon from forming.  The providers themselves don't stop a moon from forming; rather, they recycle enough debris while the battle is going on to prevent a "critical mass" of debris from being present when the battle is over (at the end of battle, chance of moon formation is calculated)

Сhance of formation of moon depends on the amount of debris in the end of the battle.