What is the lowest arithmetic sequence of positive prime integers that has 3 terms? 5 terms? 8 terms?

What is the constant difference for the lowest N positive prime integers in arithmetic sequence?

What would the first term be for such a sequence?

(A prime sequence is "lowest" if the average of its terms is the lowest. If any are tied then it is the one with the smallest starting term.)

List of intial terms and constant difference (AP) of 
Smallest Prime Arithmetic Progression of given length
of the first 21 sequence lengths (number of terms):

sequence           first prime
length       AP    of sequence
 1,           0,             2
 2,           1,             2
 3,           2,             3 <*
 4,           6,             5
 5,           6,             5 <*
 6,          30,             7
 7,         150,             7
 8,         210,           199 <*
 9,         210,           199
10,         210,           199
11,       13860,        110437
12,       13860,        110437
13,       60060,          4943
14,      420420,      31385539
15,     4144140,     115453391
16,     9699690,      53297929
17,    87297210,    3430751869
18,   717777060,    4808316343
19,  4180577390,    8287644387
20, 18846497670,  214861583621
21, 26004868890, 5749146449311

Posted by Dej Mar on 2013-03-22 09:43:43