What is the largest number of distinct positive integers you can have such that most of their pairwise differences are prime?
For example, among (2, 4, 6, 11, 13, 15) there are 15 pairwise differences, of which 10 are prime.
6-342-30-2-132 / 420-72-30 /
12-240-20-30 / 420-240 /
342-30-506-30-2-156 / 2 /
42-2-182-240-462-380 /
272-72-342-2-380-30 / 2-210-20 /
90-420-380 / 2-462-420-72-240-342:
420-240 / 6-30 / 240-342 /
210-240-420 / 420-240 / 6-30;
420-72-2-420 / 90-380 / 420-72-30 /
306-462-30-380-420-90-240-210.
~552-90-156-156-90-2-182 /
380-72-2-132-30-380-272-30-2-342-30
Note: Each letter of every word is separated by a dash and each word is separated by a slash.