Successive prime differences: Difference between revisions

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primes_less_than=: i.&.:(p:inv)

assert 2 3 5 -: primes_less_than 7

PRIMES=: primes_less_than 1e6

NB. Insert minus `-/' into the length two infixes `\'.

NB. Passive `~' swaps the arguments producing the positive differences.

SUCCESSIVE_DIFFERENCES=: 2 -~/\ PRIMES

assert 8169 -: +/ 2 = SUCCESSIVE_DIFFERENCES NB. twin prime tally

INTERVALS=: 2 ; 1 ; 2 2 ; 2 4 ; 4 2 ; 6 4 2

sequence_index=: [: I. E.

end_groups=: PRIMES {~ ({. , {:)@:] +/ i.@:>:@:#@:[

HEAD=: <;._2 'group;tally;end occurrences;'

HEAD , INTERVALS (([ ([ ; #@] ; end_groups) sequence_index)~ >)"1 0~ SUCCESSIVE_DIFFERENCES

┌─────┬─────┬───────────────────────────┐

│group│tally│end occurrences │

├─────┼─────┼───────────────────────────┤

│2 │8169 │ 3 5 │

│ │ │999959 999961 │

├─────┼─────┼───────────────────────────┤

│1 │1 │2 3 │

│ │ │2 3 │

├─────┼─────┼───────────────────────────┤

│2 2 │1 │3 5 7 │

│ │ │3 5 7 │

├─────┼─────┼───────────────────────────┤

│2 4 │1393 │ 5 7 11 │

│ │ │999431 999433 999437 │

├─────┼─────┼───────────────────────────┤

│4 2 │1444 │ 7 11 13 │

│ │ │997807 997811 997813 │

├─────┼─────┼───────────────────────────┤

│6 4 2│306 │ 31 37 41 43│

│ │ │997141 997147 997151 997153│

└─────┴─────┴───────────────────────────┘