Ormiston pairs

editable example

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ghul

use IO.Std.write_line

use Collections.LIST

use Ghul.Pipes

let limit = 10000000

let composite = LIST[bool]()

(0::limit) |> each(_ => composite.add(false))

let root mut = 2

while root * root <= limit do

if !composite[root] then

let multiple mut = root * root

while multiple <= limit do

composite[multiple] = true

multiple = multiple + root

od

fi

root = root + 1

od

digit_signature(value: int) -> string => (

let counts = LIST[int]()

for _ in 0..10 do

counts.add(0)

od

let rest mut = value

while rest > 0 do

let digit = rest % 10

counts[digit] = counts[digit] + 1

rest = rest / 10

od

let signature mut = ""

for count in counts do

signature = "{signature}{count}"

od

signature

)

let pairs = LIST[string]()

let up_to_million mut = 0

let up_to_ten_million mut = 0

let previous mut = 0

let previous_signature mut = ""

for candidate in 2..(limit + 1) do

if !composite[candidate] then

let signature = digit_signature(candidate)

if previous_signature =~ signature then

if pairs.count < 30 then

pairs.add("({previous}, {candidate})")

fi

if candidate <= 1000000 then

up_to_million = up_to_million + 1

fi

up_to_ten_million = up_to_ten_million + 1

fi

previous = candidate

previous_signature = signature

fi

od

write_line("first 30 Ormiston pairs:")

for pair in pairs do

write_line(pair)

od

write_line("{up_to_million} pairs up to 1000000")

write_line("{up_to_ten_million} pairs up to 10000000")

first 30 Ormiston pairs:
(1913, 1931)
(18379, 18397)
(19013, 19031)
(25013, 25031)
(34613, 34631)
(35617, 35671)
(35879, 35897)
(36979, 36997)
(37379, 37397)
(37813, 37831)
(40013, 40031)
(40213, 40231)
(40639, 40693)
(45613, 45631)
(48091, 48109)
(49279, 49297)
(51613, 51631)
(55313, 55331)
(56179, 56197)
(56713, 56731)
(58613, 58631)
(63079, 63097)
(63179, 63197)
(64091, 64109)
(65479, 65497)
(66413, 66431)
(74779, 74797)
(75913, 75931)
(76213, 76231)
(76579, 76597)
382 pairs up to 1000000
3722 pairs up to 10000000