`In order to accomodate the effects of chain Length involved in primecoin I propose the addition of the variables`

M = Minimum chain length accepted

T = Target chain length based on difficulty checked every block to be sure

L = Length Submitted

V = 10^((L+(T-M))/T)

V represents the value of the share

So if M = 6

Then a chain of length 6 with a chain difficulty of 9 = 10^(9/9) =1

Then a chain of length 7 with a chain difficulty of 9 = 10^(10/9) =10

Then a chain of length 8 with a chain difficulty of 9 = 10^(11/9) =100

Then a chain of length 9 with a chain difficulty of 9 = 10^(12/9) =1000

There is an error here: 10^(9/9) = 10, not 1, and so on. The results that you want will be obtained changing '/' by '-', that is:

V = 10^((L+(T-M)) - T), wich is the same as

V = 10^(L-M)

Anyway, I keep thinking that a proportional relation, like the simple V = L, will be better to minimize variance, and it will be enough to incentivate searching for longer chains.

An exponential relation, like the one that you propose, will raise very much the variance of the people submitting mostly short chains, for which it will be close to solo mining, profiting only when they are lucky. A pool must try to organize and make profitable many many small participants, instead of few big participants.

Furthermore, how do you manage the case of a chain of length 16? will it be valuated 10000000?. Exponential valuations has no sense, it raise variance for the operator and for most of the participants.