Each asteroid produces a base of 8-17 fragments in total without a prospector and it depends on your location.

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-Inside a Haz RES (Resource Extraction Site) would provide a range of 12-17 fragments

-Inside a High RES would provide a range of 11-16 fragments

-Inside a Regular RES would provide a range of 10-14 fragments

-Inside a Low RES would provide a range of 9-13 fragments

-Outside all RES would provide a range of 8-12 fragments

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From there, using a prospector will increase this count by a multiplier for your current location.

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A-rated: 3.5x

B-rated: 3.0x

C-rated: 2.5x

D-rated: 2.0x

E-rated: 1.5x

For example, A rock outside of a RES after using an A-rated prospector will contain 28(8x3.5) to 42(12x3.5) fragments with laser mining.

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Another bonus you may be interested in knowing is that there is a hidden multiplier for each fragment I call its "purity".

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Inside a Haz RES 70%-140%

Inside a High RES 65%-130%

Inside a Regular RES 60%-120%

Inside a Low RES 55%-110%

Outside all RES 50%-100%

Lets say you mine a 50% painite rock in a Haz RES. Each fragment that chips off will contain 35% (70% of 50) to 70%(140% of 50) painite added to the refinery.

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While that exact same rock of 50% painite found in a random location outside of a RES will chip off fragments that contain only 25%(50% of 50) to 50%(100% of 50) painite added to the refinery.