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.