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Tribal Primes


Your task is to find a lists of N primes such that the sums of every combination of three in the submitted list generates the most unique primes. For example, the list of 5 primes (5, 37, 47, 89, 97) generates the 9 unique primes (89, 131, 139, 149, 173, 181, 191, 223, 233). You may submit primes lists such that the largest three prime sum is less than 2 ^ 26. The contest is divided in to 20 parts where N is from 6 to 25, inclusive.

Scoring:  Your raw score for each part is the number of unique primes for that part. Your subscore is your raw score divided by the best of contest score, cubed, and then multiplied by five. If, for example, your raw score for N=6 is 12 and the best of contest raw score is 14, then your subscore would be ((12 / 14) ^ 3) * 5 = 3.1486, where the remaining decimal places are truncated. The subscores for all 20 parts are added together to compute your total score, with 100.0000 being the best possible score.

Submissions:  Submissions must contain a list of primes seperated by commas. All other characters in a submission will be ignored. A submission that contains the same prime more than once will be considered invalid.