Largest difference between adjacent primes/Factor
<lang factor>USING: arrays formatting kernel lists lists.lazy math math.order math.primes.lists sequences ;
lprimes dup cdr lzip [ first2 2dup swap - -rot 3array ] lmap-lazy [ second 1e6 < ] lwhile { 0 } [ max ] foldl
"Largest difference in adjacent primes under a million: %d between %d and %d.\n" vprintf</lang>
- Output:
Largest difference in adjacent primes under a million: 114 between 492113 and 492227.
Explanation
| Snippet | Comment | Data stack (the bottom is the top) |
|---|---|---|
| lprimes | an infinite lazy list of primes | L{ 2 3 5 7 ... } |
| dup | duplicate top of stack | L{ 2 3 5 7 ... } L{ 2 3 5 7 ... } |
| cdr | take the tail | L{ 2 3 5 7 ... } L{ 3 5 7 11 ... } |
| lzip | combine two lists into a list of pairs | L{ { 2 3 } { 3 5 } { 5 7 } { 7 11 } ... } |
| [ first2 2dup swap - -rot 3array ] | a quotation that prepends a pair's difference to itself | L{ { 2 3 } { 3 5 } { 5 7 } { 7 11 } ... } [ first2 2dup swap - -rot 3array ] |
| lmap-lazy | apply quotation lazily to each element of a list | L{ { 1 2 3 } { 2 3 5 } { 2 5 7 } { 4 7 11 } ... } |
At this point, let's take a look inside the quotation for the element { 7 11 } to see how it works.
| Snippet | Comment | Data stack (the bottom is the top) |
|---|---|---|
| { 7 11 } | ||
| first2 | place first two elements of a sequence on the data stack | 7 11 |
| 2dup | duplicate top two objects on data stack | 7 11 7 11 |
| swap | swap top two objects on data stack | 7 11 11 7 |
| - | subtract | 7 11 4 |
| -rot | put top of stack third from top | 4 7 11 |
| 3array | make a sequence from three objects | { 4 7 11 } |
Back to the regularly scheduled program...
| Snippet | Comment | Data stack (the bottom is the top) |
|---|---|---|
| L{ { 1 2 3 } { 2 3 5 } { 2 5 7 } { 4 7 11 } ... } | ||
| [ second 1e6 < ] lwhile | take from the list while the second element of each list element is less than a million | L{ { 1 2 3 } { 2 3 5 } ... { 20 999983 1000003 } } |
| { 0 } [ max ] foldl | take the maximum element, using { 0 } as a seed | { 114 492113 492227 } |
At this point, we simply use vprintf to output the answer. vprintf is like printf except it takes its arguments from a sequence instead of the data stack.