# Ormiston pairs

Ormiston pairs is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

An Ormiston pair is two consecutive prime numbers which are anagrams, i.e. contain the same decimal digits but in a different order.

(1913, 1931) is the first such pair.

Task
• Find and show the first 30 Ormiston pairs.
• Find and show the count of Ormiston pairs up to one million.

Stretch
• Find and show the count of Ormiston pairs up to ten million.

See also

## ALGOL 68

Works with: ALGOL 68G version Any - tested with release 2.8.3.win32

When running this with ALGOL 68G, you will need to specify a large heap size with e.g., `-heap 256M` on the ALGOL 68G command.

Uses the "signature" idea from the XPL0 sample and the "difference is 0 MOD 18" filter from the Wren sample.
Also shows the number of prime pairs whose difference is 0 MOD 18 but are not Ormiston pairs.

```BEGIN # find some Orimiston pairs - pairs of primes where the first and next  #
# prime are anagrams                                                    #
PR read "primes.incl.A68" PR                    # include prime utilities #
INT max prime  = 10 000 000;            # maximum number we will consider #
INT max digits = BEGIN                    # count the digits of max prime #
INT v := 1;
INT d := 1;
WHILE ( v *:= 10 ) < max prime DO d +:= 1 OD;
d
END;
[ 0 : 9 ]LONG INT dp;  # table of max digit powers for signature creation #
dp[ 0 ] := 1; FOR i TO UPB dp DO dp[ i ] := max digits * dp[ i - 1 ] OD;
[]BOOL prime      = PRIMESIEVE max prime;
# construct a list of the primes up to the maximum prime to consider      #
[]INT  prime list = EXTRACTPRIMESUPTO max prime FROMPRIMESIEVE prime;
# splits n into its digits, returning the sum of their counts, each       #
# scaled by the digit power of max digits                                 #
PROC get digits = ( INT n )LONG INT:
BEGIN
INT      v      := n;
LONG INT result := dp[ v MOD 10 ];
WHILE ( v OVERAB 10 ) > 0 DO
result +:= dp[ v MOD 10 ]
OD;
result
END # get digits # ;
# count the Ormiston pairs                                                #
INT o count := 0;
INT n count := 0;
INT p10     := 100 000;
FOR i TO UPB prime list - 1 DO
INT p1 = prime list[ i     ];
INT p2 = prime list[ i + 1 ];
IF ( p2 - p1 ) MOD 18 = 0 THEN
# p2 and p1 might be anagrams                                     #
IF get digits( p1 ) /= get digits( p2 ) THEN
# not an Ormiston pair afterall                               #
n count +:= 1
ELSE
# p1 and p2 are an Ormiston pair                              #
o count +:= 1;
IF o count <= 30 THEN
print( ( " (", whole( p1, -5 ), ", ", whole( p2, -5 ), ")"
, IF o count MOD 3 = 0 THEN newline ELSE " " FI
)
)
ELIF p1 >= p10 THEN
print( ( whole( o count - 1, -9 )
, " Ormiston pairs below "
, whole( p10, 0 )
, newline
)
);
p10 *:= 10
FI
FI
FI
OD;
print( ( whole( o count, -9 ), " Ormiston pairs below ", whole( max prime, 0 ), newline ) );
print( ( whole( n count, -9 ), " non-Ormiston ""0 MOD 18"" pairs bwlow ", whole( max prime, 0 ) ) )
END```
Output:
``` ( 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)
40 Ormiston pairs below 100000
382 Ormiston pairs below 1000000
3722 Ormiston pairs below 10000000
53369 non-Ormiston "0 MOD 18" pairs bwlow 10000000
```

## C++

Library: Primesieve
```#include <array>
#include <iomanip>
#include <iostream>
#include <utility>

#include <primesieve.hpp>

class ormiston_pair_generator {
public:
ormiston_pair_generator() { prime_ = pi_.next_prime(); }
std::pair<uint64_t, uint64_t> next_pair() {
for (;;) {
uint64_t prime = prime_;
auto digits = digits_;
prime_ = pi_.next_prime();
digits_ = get_digits(prime_);
if (digits_ == digits)
return std::make_pair(prime, prime_);
}
}

private:
static std::array<int, 10> get_digits(uint64_t n) {
std::array<int, 10> result = {};
for (; n > 0; n /= 10)
++result[n % 10];
return result;
}
primesieve::iterator pi_;
uint64_t prime_;
std::array<int, 10> digits_;
};

int main() {
ormiston_pair_generator generator;
int count = 0;
std::cout << "First 30 Ormiston pairs:\n";
for (; count < 30; ++count) {
auto [p1, p2] = generator.next_pair();
std::cout << '(' << std::setw(5) << p1 << ", " << std::setw(5) << p2
<< ')' << ((count + 1) % 3 == 0 ? '\n' : ' ');
}
std::cout << '\n';
for (uint64_t limit = 1000000; limit <= 1000000000; ++count) {
auto [p1, p2] = generator.next_pair();
if (p1 > limit) {
std::cout << "Number of Ormiston pairs < " << limit << ": " << count
<< '\n';
limit *= 10;
}
}
}
```
Output:
```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)

Number of Ormiston pairs < 1000000: 382
Number of Ormiston pairs < 10000000: 3722
Number of Ormiston pairs < 100000000: 34901
Number of Ormiston pairs < 1000000000: 326926
```

## F#

This task uses Extensible Prime Generator (F#)

```// Ormiston pairs. Nigel Galloway: January 31st., 2023
let fG(n,g)=let i=Array.zeroCreate<int>10
let rec fG n g=if g<10 then i[g]<-n i[g] 1 else i[g%10]<-n i[g%10] 1; fG n (g/10)
fG (+) n; fG (-) g; Array.forall ((=)0) i
let oPairs n=n|>Seq.pairwise|>Seq.filter fG
primes32()|>oPairs|>Seq.take 30|>Seq.iter(printf "%A "); printfn ""
printfn \$"<1 million: %d{primes32()|>Seq.takeWhile((>)1000000)|>oPairs|>Seq.length}"
printfn \$"<10 million: %d{primes32()|>Seq.takeWhile((>)10000000)|>oPairs|>Seq.length}"
printfn \$"<100 million: %d{primes32()|>Seq.takeWhile((>)100000000)|>oPairs|>Seq.length}"
printfn \$"<1 billion: %d{primes32()|>Seq.takeWhile((>)1000000000)|>oPairs|>Seq.length}"
```
Output:
```(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)
<1 million: 382
<10 million: 3722
<100 million: 34901
<1 billion: 326926
```

## Factor

Works with: Factor version 0.99 2022-04-03
```USING: grouping io kernel lists lists.lazy math math.parser
math.primes.lists math.statistics prettyprint sequences ;

: ormistons ( -- list )
lprimes dup cdr lzip
[ first2 [ >dec histogram ] same? ] lfilter ;

"First 30 Ormiston pairs:" print
30 ormistons ltake list>array 5 group simple-table. nl

ormistons [ first 1e6 < ] lwhile llength pprint bl
"Ormiston pairs less than a million." print
```
Output:
```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 Ormiston pairs less than a million.
```

## FreeBASIC

Translation of: XPL0
```#include "isprime.bas"

Function GetSig(Byval N As Integer) As Integer
Dim As Integer Sig = 0
Do While N > 0
Sig += 1 Shl (N Mod 10)
N \= 10
Loop
Return Sig
End Function

Dim As Integer Cnt = 0, N0 = 0, Sig0 = 0, N = 3, Sig
Do
If isPrime(N) Then
Sig = GetSig(N)
If Sig = Sig0 Then
Cnt += 1
If Cnt <= 30 Then
Print Using "##### #####"; N0; N;
If Cnt Mod 3 = 0 Then Print Else Print "   ";
End If
End If
Sig0 = Sig
N0 = N
End If
If N = 1e5 -1 Then Print !"\nOrmiston pairs up to one hundred thousand: "; Cnt
If N = 1e6 -1 Then Print "Ormiston pairs up to one million: "; Cnt
If N = 1e7 -1 Then Print "Ormiston pairs up to ten million: "; Cnt: Exit Do
N += 2
Loop

Sleep
```
Output:
```  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

Ormiston pairs up to one hundred thousand:  40
Ormiston pairs up to one million: 382
Ormiston pairs up to ten million: 3722```

## Go

Translation of: Wren
Library: Go-rcu
```package main

import (
"fmt"
"rcu"
)

func main() {
const limit = 1e9
primes := rcu.Primes(limit)
var orm30 [][2]int
j := int(1e5)
count := 0
var counts []int
for i := 0; i < len(primes)-1; i++ {
p1 := primes[i]
p2 := primes[i+1]
if (p2-p1)%18 != 0 {
continue
}
key1 := 1
for _, dig := range rcu.Digits(p1, 10) {
key1 *= primes[dig]
}
key2 := 1
for _, dig := range rcu.Digits(p2, 10) {
key2 *= primes[dig]
}
if key1 == key2 {
if count < 30 {
orm30 = append(orm30, [2]int{p1, p2})
}
if p1 >= j {
counts = append(counts, count)
j *= 10
}
count++
}
}
counts = append(counts, count)
fmt.Println("First 30 Ormiston pairs:")
for i := 0; i < 30; i++ {
fmt.Printf("%5v ", orm30[i])
if (i+1)%3 == 0 {
fmt.Println()
}
}
fmt.Println()
j = int(1e5)
for i := 0; i < len(counts); i++ {
fmt.Printf("%s Ormiston pairs before %s\n", rcu.Commatize(counts[i]), rcu.Commatize(j))
j *= 10
}
}
```
Output:
```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]

40 Ormiston pairs before 100,000
382 Ormiston pairs before 1,000,000
3,722 Ormiston pairs before 10,000,000
34,901 Ormiston pairs before 100,000,000
326,926 Ormiston pairs before 1,000,000,000
```

## J

For this, we would like to be able to test if a prime number is the first value in an Ormiston pair:

```   isorm=: -:&(/:~)&":&> 4 p: ]
```

We could also use a routine to organize pairs of numbers as moderate width lines of text:

```   fmtpairs=: {{ names <@([,',',])&":/"1 y}}
```

Then the task becomes:

```   fmtpairs (,. 4 p:]) p:30{.I. isorm i.&.(p:inv) 1e6
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
+/isorm i.&.(p:inv) 1e6   NB. number of Ormiston pairs less than 1e6
382
+/isorm i.&.(p:inv) 1e7   NB. number of Ormiston pairs less than 1e7
3722
```

## jq

Works with: jq

Preliminaries

```# Assuming . > 2, return an array, \$a, of length .+1 such that
# \$a[\$i] is \$i if \$i is prime, and null otherwise.
def primeSieve:
# erase(i) sets .[i*j] to false for integral j > 1
def erase(i):
if .[i] then
reduce range(2; (1 + length) / i) as \$j (.; .[i * \$j] = null)
else .
end;
(. + 1) as \$n
| ((\$n|sqrt) / 2) as \$s
| [null, null, range(2; \$n)]
| reduce (2, 1 + (2 * range(1; \$s))) as \$i (.; erase(\$i)) ;```

The Task

```def digits: tostring | explode;

def ormiston_pairs(\$limit):
(\$limit | primeSieve | map(select(.))) as \$primes
| range(0; \$primes|length-1) as \$i
| \$primes[\$i]   as \$p1
| \$primes[\$i+1] as \$p2
| select( (\$p2|digits|sort) == (\$p1|digits|sort) )
| [\$p1, \$p2] ;

def task(\$limit):
reduce ormiston_pairs(\$limit) as \$pair (
{count:0, orm30: [], counts: [], j: 1e5};
if .count < 30 then .orm30 += [\$pair] else . end
| if \$pair[0] >= .j
then .counts += [.count]
| .j *= 10
else .
end
| .count += 1 )
| .counts += [.count]
| ("First 30 Ormiston pairs:", (.orm30 | map(tostring) | _nwise(3) | join(" "))),
"",
foreach range(0; .counts|length) as \$i (.j = 1e5;
.emit = "\(.counts[\$i]) Ormiston pairs before \(.j)"
| .j *= 10;
select(.emit).emit) );

task(1e7) # ten million```
Output:
```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]

40 Ormiston pairs before 100000
382 Ormiston pairs before 1000000
3722 Ormiston pairs before 10000000
```

## Pascal

### Free Pascal

//update the digits by adding difference.// Using MOD 18 = 0 and convert is faster.

```program Ormiston;
{\$IFDEF FPC}{\$MODE DELPHI} {\$OPTIMIZATION ON,ALL}{\$ENDIF}
{\$IFDEF WINDOWS}{\$APPLICATION CONSOLE}{\$ENDIF}

uses
sysutils,strUtils;

//********* segmented sieve of erathostenes *********
{segmented sieve of Erathostenes using only odd numbers}
{using presieved sieve of small primes, to reduce the most time consuming}
const
smlPrimes :array [0..10] of Byte = (2,3,5,7,11,13,17,19,23,29,31);
maxPreSievePrimeNum = 8;
maxPreSievePrime = 19;//smlPrimes[maxPreSievePrimeNum];
cSieveSize = 2*16384;//<= High(Word)+1 // Level I Data Cache
type
tSievePrim = record
svdeltaPrime:word;//diff between actual and new prime
svSivOfs:word;    //Offset in sieve
svSivNum:LongWord;//1 shl (1+16+32) = 5.6e14
end;
tpSievePrim = ^tSievePrim;

var
//sieved with primes 3..maxPreSievePrime.here about 255255 Byte
{\$ALIGN 32}
preSieve :array[0..3*5*7*11*13*17*19-1] of Byte;//must be > cSieveSize
{\$ALIGN 32}
Sieve :array[0..cSieveSize-1] of Byte;
{\$ALIGN 32}
//prime = FoundPrimesOffset + 2*FoundPrimes[0..FoundPrimesCnt]
FoundPrimes : array[0..12252] of Word;
{\$ALIGN 32}
sievePrimes : array[0..1077863] of tSievePrim;
FoundPrimesOffset : Uint64;
FoundPrimesCnt,
FoundPrimesIdx,
FoundPrimesTotal,
SieveNum,
SieveMaxIdx,
preSieveOffset,
LastInsertedSievePrime :NativeUInt;

procedure CopyPreSieveInSieve; forward;
procedure CollectPrimes; forward;
procedure sieveOneSieve; forward;
procedure Init0Sieve; forward;
procedure SieveOneBlock; forward;

procedure preSieveInit;
var
i,pr,j,umf : NativeInt;
Begin
fillchar(preSieve[0],SizeOf(preSieve),#1);
i := 1;
pr := 3;// starts with pr = 3
umf := 1;
repeat
IF preSieve[i] =1 then
Begin
pr := 2*i+1;
j := i;
repeat
preSieve[j] := 0;
inc(j,pr);
until j> High(preSieve);
umf := umf*pr;
end;
inc(i);
until (pr = maxPreSievePrime)OR(umf>High(preSieve)) ;
preSieveOffset := 0;
end;

function InsertSievePrimes(PrimPos:NativeInt):NativeInt;
var
j    :NativeUINt;
i,pr : NativeUInt;
begin
i := 0;
//ignore first primes already sieved with
if SieveNum = 0 then
i := maxPreSievePrimeNum;
pr :=0;
j := Uint64(SieveNum)*cSieveSize*2-LastInsertedSievePrime;
with sievePrimes[PrimPos] do
Begin
pr := FoundPrimes[i]*2+1;
svdeltaPrime := pr+j;
j := pr;
end;
inc(PrimPos);
for i := i+1 to FoundPrimesCnt-1 do
Begin
IF PrimPos > High(sievePrimes) then
BREAK;
with sievePrimes[PrimPos] do
Begin
pr := FoundPrimes[i]*2+1;
svdeltaPrime := (pr-j);
j := pr;
end;
inc(PrimPos);
end;
LastInsertedSievePrime :=Uint64(SieveNum)*cSieveSize*2+pr;
result := PrimPos;
end;

procedure CalcSievePrimOfs(lmt:NativeUint);
//lmt High(sievePrimes)
var
i,pr : NativeUInt;
sq : Uint64;
begin
pr := 0;
i := 0;
repeat
with sievePrimes[i] do
Begin
pr := pr+svdeltaPrime;
IF sqr(pr)  < (cSieveSize*2) then
Begin
svSivNum := 0;
svSivOfs := (pr*pr-1) DIV 2;
end
else
Begin
SieveMaxIdx := i;
pr := pr-svdeltaPrime;
BREAK;
end;
end;
inc(i);
until i > lmt;

for i := i to lmt do
begin
with sievePrimes[i] do
Begin
pr := pr+svdeltaPrime;
sq := sqr(pr);
svSivNum := sq DIV (2*cSieveSize);
svSivOfs := ( (sq - Uint64(svSivNum)*(2*cSieveSize))-1)DIV 2;
end;
end;
end;

procedure sievePrimesInit;
var
i,j,pr,PrimPos:NativeInt;
Begin
LastInsertedSievePrime := 0;
preSieveOffset := 0;
SieveNum :=0;
CopyPreSieveInSieve;
//normal sieving of first sieve
i := 1; // start with 3
repeat
while Sieve[i] = 0 do
inc(i);
pr := 2*i+1;
inc(i);
j := ((pr*pr)-1) DIV 2;
if j > High(Sieve) then
BREAK;
repeat
Sieve[j] := 0;
inc(j,pr);
until j > High(Sieve);
until false;

CollectPrimes;
PrimPos := InsertSievePrimes(0);
LastInsertedSievePrime := FoundPrimes[PrimPos]*2+1;

IF PrimPos < High(sievePrimes) then
Begin
Init0Sieve;
sieveOneBlock;
repeat
sieveOneBlock;
dec(SieveNum);
PrimPos := InsertSievePrimes(PrimPos);
inc(SieveNum);
until PrimPos > High(sievePrimes);
end;
Init0Sieve;
end;

procedure Init0Sieve;
begin
FoundPrimesTotal :=0;
preSieveOffset := 0;
SieveNum :=0;
CalcSievePrimOfs(High(sievePrimes));
end;

procedure CopyPreSieveInSieve;
var
lmt : NativeInt;
Begin
lmt := preSieveOffset+cSieveSize;
lmt := lmt-(High(preSieve)+1);
IF lmt<= 0 then
begin
Move(preSieve[preSieveOffset],Sieve[0],cSieveSize);
if lmt <> 0 then
inc(preSieveOffset,cSieveSize)
else
preSieveOffset := 0;
end
else
begin
Move(preSieve[preSieveOffset],Sieve[0],cSieveSize-lmt);
Move(preSieve[0],Sieve[cSieveSize-lmt],lmt);
preSieveOffset := lmt
end;
end;

procedure sieveOneSieve;
var
sp:tpSievePrim;
pSieve :pByte;
i,j,pr,sn,dSievNum :NativeUint;
Begin
pr := 0;
sn := sieveNum;
sp := @sievePrimes[0];
pSieve := @Sieve[0];
For i := SieveMaxIdx downto 0 do
with sp^ do
begin
pr := pr+svdeltaPrime;
IF svSivNum = sn then
Begin
j := svSivOfs;
repeat
pSieve[j] := 0;
inc(j,pr);
until j > High(Sieve);
dSievNum := j DIV cSieveSize;
svSivOfs := j-dSievNum*cSieveSize;
svSivNum := sn+dSievNum;
end;
inc(sp);
end;
i := SieveMaxIdx+1;
repeat
if i > High(SievePrimes) then
BREAK;
with sp^ do
begin
if svSivNum > sn then
Begin
SieveMaxIdx := I-1;
Break;
end;
pr := pr+svdeltaPrime;
j := svSivOfs;
repeat
Sieve[j] := 0;
inc(j,pr);
until j > High(Sieve);
dSievNum := j DIV cSieveSize;
svSivOfs := j-dSievNum*cSieveSize;
svSivNum := sn+dSievNum;
end;
inc(i);
inc(sp);
until false;
end;

procedure CollectPrimes;
//extract primes to FoundPrimes
var
pSieve : pbyte;
pFound : pWord;
i,idx : NativeUint;
Begin
FoundPrimesOffset := SieveNum*2*cSieveSize;
FoundPrimesIdx := 0;
pFound :=@FoundPrimes[0];
i := 0;
idx := 0;
IF SieveNum = 0 then
//include small primes used to pre-sieve
Begin
repeat
pFound[idx]:= (smlPrimes[idx]-1) DIV 2;
inc(idx);
until smlPrimes[idx]>maxPreSievePrime;
i := (smlPrimes[idx] -1) DIV 2;
end;
//grabbing the primes without if then -> reduces time extremly
//primes are born to let branch-prediction fail.
pSieve:= @Sieve[Low(Sieve)];
repeat
//store every value until a prime aka 1 is found
pFound[idx]:= i;
inc(idx,pSieve[i]);
inc(i);
until i>High(Sieve);
FoundPrimesCnt:= idx;
inc(FoundPrimesTotal,Idx);
end;

procedure SieveOneBlock;
begin
CopyPreSieveInSieve;
sieveOneSieve;
CollectPrimes;
inc(SieveNum);
end;

function Nextprime:Uint64;
Begin
result := FoundPrimes[FoundPrimesIdx]*2+1+FoundPrimesOffset;
if (FoundPrimesIdx=0) AND (sievenum = 1) then
inc(result);
inc(FoundPrimesIdx);
If FoundPrimesIdx>= FoundPrimesCnt then
SieveOneBlock;
end;

function PosOfPrime: Uint64;inline;
Begin
result := FoundPrimesTotal-FoundPrimesCnt+FoundPrimesIdx;
end;

function TotalCount :Uint64;inline;
begin
result := FoundPrimesTotal;
end;

function SieveSize :LongInt;inline;
Begin
result := 2*cSieveSize;
end;

function SieveStart:Uint64;inline;
Begin
result := (SieveNum-1)*2*cSieveSize;
end;

procedure InitPrime;
Begin
Init0Sieve;
SieveOneBlock;
end;
//********* segmented sieve of erathostenes *********

const
Limit= 10*1000*1000*1000;
type
tDigits10 = array[0..15] of byte;
td10_UsedDgts2 = array[0..3] of  Uint32;
td10_UsedDgts3 = array[0..1] of  Uint64;
tpd10_UsedDgts3 = ^td10_UsedDgts3;

procedure OutIn(cnt,p1,p2:NativeInt);
Begin
write('[',Numb2USA(IntToStr(p1)):6,'|',Numb2USA(IntToStr(p2)):6,']');
if cnt MOD 5 = 0 then
writeln;
end;

function OutByPot10(cnt,prLimit:NativeInt):NativeInt;
Begin
writeln(Numb2USA(IntToStr(cnt)):12,' Ormiston pairs before ',Numb2USA(IntToStr(prLimit)):14);
result := 10*prLimit;
end;

procedure Convert2Digits10(p:NativeUint;var outP:tDigits10);
var
r : NativeUint;
begin
// fillchar(outP,SizeOf(outP),#0);//takes longer
td10_UsedDgts3(outP)[0]:=0;td10_UsedDgts3(outP)[1]:=0;
repeat
r := p DIV 10;
inc(outP[p-10*r]);
p := r;
until r = 0;
end;

function CheckOrmiston(const d1,d2:tpd10_UsedDgts3):boolean;inline;
begin
result := (d1^[0]=d2^[0]) AND (d1^[1]=d2^[1]);
end;

var
{\$align 16}
p1,p2 :tDigits10;
pr,pr1,prLimit :nativeInt;
cnt : NativeUint;
Begin
preSieveInit;
sievePrimesInit;
InitPrime;

prLimit := 100*1000;
cnt := 0;
pr1 := nextprime;
repeat
pr := nextprime;
if pr > limit then
BREAK;
if (pr-pr1) mod 18 = 0  then
begin
Convert2Digits10(pr1,p1);
Convert2Digits10(pr,p2);
if CheckOrmiston(@p1,@p2) then
begin
inc(cnt);
IF cnt <= 30 then
OutIn(cnt,pr1,pr);
end;
end;
if pr >=prLimit then
prlimit:= OutByPot10(cnt,prlimit);
pr1:= pr;
until false;
OutByPot10(cnt,prlimit);
end.
```
@TIO.RUN:
```//only get all primes to 1E10 Real time: 13.294 s CPU share: 99.11 %
[ 1,913| 1,931][18,379|18,397][19,013|19,031][25,013|25,031][34,613|34,631]
[35,617|35,671][35,879|35,897][36,979|36,997][37,379|37,397][37,813|37,831]
[40,013|40,031][40,213|40,231][40,639|40,693][45,613|45,631][48,091|48,109]
[49,279|49,297][51,613|51,631][55,313|55,331][56,179|56,197][56,713|56,731]
[58,613|58,631][63,079|63,097][63,179|63,197][64,091|64,109][65,479|65,497]
[66,413|66,431][74,779|74,797][75,913|75,931][76,213|76,231][76,579|76,597]
40 Ormiston pairs before        100,000
382 Ormiston pairs before      1,000,000
3,722 Ormiston pairs before     10,000,000
34,901 Ormiston pairs before    100,000,000
326,926 Ormiston pairs before  1,000,000,000
3,037,903 Ormiston pairs before 10,000,000,000
Real time: 21.114 s User time: 20.862 s Sys. time: 0.057 s CPU share: 99.07 %
@home real	0m6,873s user	0m6,864s sys	0m0,008s
```

## Phix

Translation of: Wren
```with javascript_semantics
atom t0 = time(),
t1 = time()+1
constant limit = iff(platform()=JS?1e8:1e9), -- (keep JS<10s)
primes = get_primes_le(limit)
sequence orm30 = {}, counts = {}
integer count = 0, nc = 1e5
for i=1 to length(primes)-1 do
integer p1 = primes[i],
p2 = primes[i+1]
if remainder(p2-p1,18)=0
and sort(sprint(p1))=sort(sprint(p2)) then
if count<30 then
orm30 &= {sprintf("[%5d %5d]",{p1, p2})}
end if
if p1>=nc then
counts &= count
nc *= 10
end if
count += 1
end if
if time()>t1 then
progress("%d/%d\r",{i,length(primes)})
t1 = time()+1
end if
end for
progress("")
counts &= count
printf(1,"First 30 Ormiston pairs:\n%s\n",join_by(orm30,1,3))
for i,c in counts do
printf(1,"%,d Ormiston pairs before %,d\n", {c, power(10,i+4)})
end for
?elapsed(time()-t0)
```
Output:
```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]

40 Ormiston pairs before 100,000
382 Ormiston pairs before 1,000,000
3,722 Ormiston pairs before 10,000,000
34,901 Ormiston pairs before 100,000,000
326,926 Ormiston pairs before 1,000,000,000
"39.8s"
```

### slower but higher limits

```--
-- demo\rosetta\Ormiston_pairs.exw
-- ===============================
--
--  Uses a segmented sieve, which is about half the speed of get_primes_le(), but uses far less memory
--  If permited, get_primes_le(1e10) would generate a result of 455,052,511 primes, more than 32 bit
--  can cope with, and use over 6GB of ram, and take about 11mins 44s, that is on this box at least,
--  whereas this processes them on-the-fly, and only uses about 6MB of memory (ie 0.1% of 6GB).
--
with javascript_semantics

atom t0 = time()

procedure ormiston_pairs(atom limit)
// Generate primes using the segmented sieve of Eratosthenes.
// credit: https://gist.github.com/kimwalisch/3dc39786fab8d5b34fee
integer segment_size = floor(sqrt(limit)),
count = 0, i = 3, s = 3
atom p1 = 2, n = 3, nc = 1e5, low = 0, t1 = time()+1

sequence isprime = repeat(true,segment_size+1),
primes = {},
multiples = {},
orm30 = repeat(0,30)

while low<=limit do
sequence sieve = repeat(true,segment_size+1)
if time()>t1 then
progress("Processing %,d/%,d (%3.2f%%)\r",{low,limit,(low/limit)*100})
t1 = time()+1
end if

// current segment = [low, high]
atom high = min(low+segment_size,limit)
// generate sieving primes using simple sieve of Eratosthenes
while i*i<=min(high,segment_size) do
if isprime[i+1] then
for j=i*i to segment_size by i do
isprime[j+1] = false
end for
end if
i += 2
end while

// initialize sieving primes for segmented sieve
while s*s<=high do
if isprime[s+1] then
primes &= s
multiples &= s*s-low
end if
s += 2
end while

// sieve the current segment
for mi,j in multiples do
integer k = primes[mi]*2
while j<segment_size do
sieve[j+1] = false
j += k
end while
multiples[mi] = j - segment_size
end for

while n<=high do
if sieve[n-low+1] then // n is a prime
if remainder(n-p1,18)=0
and sort(sprint(p1))=sort(sprint(n)) then
if p1>=nc then
string e = elapsed_short(time()-t0)
progress("%,d Ormiston pairs before %,d (%s)\n", {count, nc, e})
nc *= 10
end if
count += 1
if count<=30 then
orm30[count] = sprintf("[%5d %5d]",{p1, n})
if count=30 then
printf(1,"First 30 Ormiston pairs:\n%s\n",join_by(orm30,1,3))
end if
end if
end if
p1 = n
end if
n += 2
end while
low += segment_size
end while
string e = elapsed_short(time()-t0)
progress("%,d Ormiston pairs before %,d (%s)\n", {count, nc, e})
end procedure
ormiston_pairs(iff(platform()=JS?1e8:1e9))
```
Output:

With limit upped to 1e10

```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]

40 Ormiston pairs before 100,000 (0s)
382 Ormiston pairs before 1,000,000 (0s)
3,722 Ormiston pairs before 10,000,000 (0s)
34,901 Ormiston pairs before 100,000,000 (5s)
326,926 Ormiston pairs before 1,000,000,000 (55s)
3,037,903 Ormiston pairs before 10,000,000,000 (21:57)
```

Note that running this under pwa/p2js with a limit of 1e9 would get you a blank screen for 1min 25s, hence I've limited it to 1e8 (8s)
I have not the patience to see whether JavaScript would actually cope with 1e10, but it should (with a blank screen for at least half an hour).

## Python

```""" rosettacode.org task Ormiston_pairs """

from sympy import primerange

PRIMES1M = list(primerange(1, 1_000_000))
ASBASE10SORT = [str(sorted(list(str(i)))) for i in PRIMES1M]
ORMISTONS = [(PRIMES1M[i - 1], PRIMES1M[i]) for i in range(1, len(PRIMES1M))
if ASBASE10SORT[i - 1] == ASBASE10SORT[i]]

print('First 30 Ormiston pairs:')
for (i, o) in enumerate(ORMISTONS):
if i < 30:
print(f'({o[0] : 6} {o[1] : 6} )',
end='\n' if (i + 1) % 5 == 0 else '  ')
else:
break

print(len(ORMISTONS), 'is the count of Ormiston pairs up to one million.')
```
Output:
```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 is the count of Ormiston pairs up to one million.
```

## Raku

```use Lingua::EN::Numbers;
use List::Divvy;

my @primes = lazy (^∞).hyper.grep( &is-prime ).map: { \$_ => .comb.sort.join };
my @Ormistons = @primes.kv.map: { (\$^value.key, @primes[\$^key+1].key) if \$^value.value eq @primes[\$^key+1].value };

say "First thirty Ormiston pairs:";
say @Ormistons[^30].batch(3)».map( { "({.[0].fmt: "%5d"}, {.[1].fmt: "%5d"})" } ).join: "\n";
say '';
say +@Ormistons.&before( *[1] > \$_ ) ~ " Ormiston pairs before " ~ .Int.&cardinal for 1e5, 1e6, 1e7;
```
Output:
```First thirty 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)

40 Ormiston pairs before one hundred thousand
382 Ormiston pairs before one million
3722 Ormiston pairs before ten million```

## Rust

```// [dependencies]
// primal = "0.3"

fn get_digits(mut n: usize) -> [usize; 10] {
let mut digits = [0; 10];
while n > 0 {
digits[n % 10] += 1;
n /= 10;
}
digits
}

fn ormiston_pairs() -> impl std::iter::Iterator<Item = (usize, usize)> {
let mut digits = [0; 10];
let mut prime = 0;
let mut primes = primal::Primes::all();
std::iter::from_fn(move || {
for p in primes.by_ref() {
let prime0 = prime;
prime = p;
let digits0 = digits;
digits = get_digits(prime);
if digits == digits0 {
return Some((prime0, prime));
}
}
None
})
}

fn main() {
let mut count = 0;
let mut op = ormiston_pairs();
println!("First 30 Ormiston pairs:");
for (p1, p2) in op.by_ref() {
count += 1;
let c = if count % 3 == 0 { '\n' } else { ' ' };
print!("({:5}, {:5}){}", p1, p2, c);
if count == 30 {
break;
}
}
println!();
let mut limit = 1000000;
for (p1, _) in op.by_ref() {
if p1 > limit {
println!("Number of Ormiston pairs < {}: {}", limit, count);
limit *= 10;
if limit == 10000000000 {
break;
}
}
count += 1;
}
}
```
Output:
```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)

Number of Ormiston pairs < 1000000: 382
Number of Ormiston pairs < 10000000: 3722
Number of Ormiston pairs < 100000000: 34901
Number of Ormiston pairs < 1000000000: 326926
```

## Wren

Library: Wren-math
Library: Wren-fmt
```import "./math" for Int
import "./fmt" for Fmt

var limit = 1e9
var primes = Int.primeSieve(limit)
var orm30 = []
var j = 1e5
var count = 0
var counts = []
for (i in 0...primes.count-1) {
var p1 = primes[i]
var p2 = primes[i+1]
if ((p2 - p1) % 18 != 0) continue
var key1 = 1
for (dig in Int.digits(p1)) key1 = key1 * primes[dig]
var key2 = 1
for (dig in Int.digits(p2)) key2 = key2 * primes[dig]
if (key1 == key2) {
if (count < 30) orm30.add([p1, p2])
if (p1 >= j) {
counts.add(count)
j = j * 10
}
count = count + 1
}
}
counts.add(count)
System.print("First 30 Ormiston pairs:")
Fmt.tprint("[\$,6d] ", orm30, 3)
System.print()
j = 1e5
for (i in 0...counts.count) {
Fmt.print("\$,d Ormiston pairs before \$,d",  counts[i], j)
j = j * 10
}
```
Output:
```First 30 Ormiston pairs:
[ 1,913  1,931]  [18,379 18,397]  [19,013 19,031]
[25,013 25,031]  [34,613 34,631]  [35,617 35,671]
[35,879 35,897]  [36,979 36,997]  [37,379 37,397]
[37,813 37,831]  [40,013 40,031]  [40,213 40,231]
[40,639 40,693]  [45,613 45,631]  [48,091 48,109]
[49,279 49,297]  [51,613 51,631]  [55,313 55,331]
[56,179 56,197]  [56,713 56,731]  [58,613 58,631]
[63,079 63,097]  [63,179 63,197]  [64,091 64,109]
[65,479 65,497]  [66,413 66,431]  [74,779 74,797]
[75,913 75,931]  [76,213 76,231]  [76,579 76,597]

40 Ormiston pairs before 100,000
382 Ormiston pairs before 1,000,000
3,722 Ormiston pairs before 10,000,000
34,901 Ormiston pairs before 100,000,000
326,926 Ormiston pairs before 1,000,000,000
```

## XPL0

```func IsPrime(N);        \Return 'true' if N is prime
int  N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];

func GetSig(N);         \Return signature of N
\A "signature" is the count of each digit in N packed into a 32-bit word
int N, Sig;
[Sig:= 0;
repeat  N:= N/10;
Sig:= Sig + 1<<(rem(0)*3);
until   N = 0;
return Sig;
];

int Cnt, N, N0, Sig, Sig0;
[Cnt:= 0;  N0:= 0;  Sig0:= 0;  N:= 3;
Format(6, 0);
loop    [if IsPrime(N) then
[Sig:= GetSig(N);
if Sig = Sig0 then
[Cnt:= Cnt+1;
if Cnt <= 30 then
[RlOut(0, float(N0));  RlOut(0, float(N));
if rem(Cnt/3) = 0 then CrLf(0) else Text(0, "  ");
];
];
Sig0:= Sig;
N0:= N;
];
if N = 1_000_000-1 then
[Text(0, "^m^jOrmiston pairs up to one million: ");
IntOut(0, Cnt);
];
if N = 10_000_000-1 then
[Text(0, "^m^jOrmiston pairs up to ten million: ");
IntOut(0, Cnt);
quit;
];
N:= N+2;
];
]```
Output:
```  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

Ormiston pairs up to one million: 382
Ormiston pairs up to ten million: 3722```