It's good to have a top priority.

It's good to have a top 3 priorities.

Can this pattern be extended? One pattern is to make a top-N priorities where N is each prime up to some prime K. The idea is that the priorities up to each prime are more important than later priorities, but you don't have to decide beyond that which are more important than others. E.g. for K = 7:

Priority 1:

- Eat

Priorities 2 thru 3:

- Pay electricity bill
- Go thru email

Priorities 4 thru 5:

- Wash the dog
- Do the laundry

Priorities 6 thru 7:

- Shop for new sofa
- Read a book

the idea is that eating is a higher priority than paying the electricity bill, and paying the bill is a higher priority than washing the dog, but paying the electricity bill and going thru email are about equal priority.

Instead of primes, you could do arithmatically or geometrically increase the number of items in each group. Arithmatically, you could have 1 item, then 2 items in the second group, then 3 items in the third group, then 4 items, etc. Geometrically, using base 2, you could have 1 item, then (4 - 1 =) 3 items in the second group, then (8 - 4 = ) 4 items in the third group, then (16 - 8 =) 8 items, etc.

using base e and rounding, you could have 1 item, then (round(e - 1) = ) 2 items, then (round(e^2 - (1 + 2)) = ) 4 items, then (round(e^3 - (1+2+4)) = ) 13 items, then (round(e^4 - (1+2+4+13)) = ) 35 items, etc.

The prime approach has too many small steps, especially intervals of length 2. The geometric-with-base-e approach seems good, but in many cases you want more differentiation among those 13 items.

Another approach would be to do primes, but only those primes whose distance from the previous admitted prime is greater than previous admitted intervals. E.g. 1, 3, (5 is not admitted because the 5 - 3 is only 2, and we already had an interval of length 2 between 3 and 1), 7 (the interval between 7 and 3 is 4; the interval between 7 and 5 doesn't matter because 5 was not admitted), (11 is not admitted because 11 - 7 is only 4), 13 (the interval between 7 and 13 is 6), (17 is not admitted because 17 - 13 is only 4), (19 is not admitted because 19 - 13 is only 6), 23 (the interval between 23 and 13 is 10), (29 is not admitted because 29 - 23 is only 6), (31 is not admitted because 31 - 23 is only 8), 37 (37 - 23 = 14), ...

In short, the numbers are 1, 3, 7, 13, 23, 37, 53, 71, 97, ... . The intervals (number of items in each set) are 1, 2, 4, 6, 10, 14, 16, 18, 26 (note: this sequence is https://oeis.org/A075574 ).

I (somewhat confusingly) call this last method the 'prime priority' method.

The 'prime priority' method can be elaborated by making two separate lists of 'major priorities' and 'minor priorities'. When this is done, the numbers per group for the minor priorities are doubled (to 2, 4, 8, 12, 20, 28, etc) because if priority types were themselves in a list of 'prime priority' groupings, there would be one group containing only the type 'major priority', and then two 'minor priority' types in the second group. One could even extend this to a third list (tertiary? tangential? peripheral? incidental? ancillary? side? subsidiary? accessory? auxillary? satellite? junior (e.g. ruling/senior/junior)? light? subaltern (e.g. main/alternate/subalternate)? supplementary? quick google searches for 'major minor x' reveal that supplementary and auxiliary seem to be most used for a third step after major/minor. i'll choose 'supplementary'), 'supplementary priorities', in which the intervals are quadrupled: 4, 8, 16, 24, 40, 56, ....

You could also consider having a major, minor, and supplementary list, and limiting each to 3 groups, or at least marking the boundary after the third group as the 'horizon' of things that you can reasonably consider; or, to have a major and minor list, and put the horizon after the first 2 groups. Or, you could place the horizon differently, placing it after the third group for majors, after the second for minors, and after the first for supplementaries, for a total of (7 + 6 + 4 = 17).

(as a matter of number theory/numerology it also may be interesting to consider the unions and intersection of such lists, and to consider to what extent this can serve as an alternative to prime number factorization for characterization of all integers, and to explore whether the total 7+6+4, which is prime, and which is similar to (3 + 2 = 5) if you started with 2 instead of 3), remains prime if you extend that pattern to larger numbers, and if they remain primes that were skipped in the initial sequence, but i digress...)