Quadrat special primes: Difference between revisions
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;Task:
Find the sequence of increasing primes, q, from 2 up to but excluding '''16,000''',
where the successor of q is the least prime, p, such that p - q is a perfect square.
<br><br>
=={{header|11l}}==
{{trans|Nim}}
<syntaxhighlight lang="11l">F is_prime(n)
I n == 2
R 1B
I n < 2 | n % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(n))).step(2)
I n % i == 0
R 0B
R 1B
V Max = 16'000
V quadraPrimes = [2, 3]
V n = 3
L
L(i) (2 .. Int(sqrt(Max))).step(2)
V next = n + i * i
I next >= Max
^L.break
I is_prime(next)
n = next
quadraPrimes [+]= n
L.break
print(‘Quadrat special primes < 16000:’)
L(qp) quadraPrimes
print(‘#5’.format(qp), end' I (L.index + 1) % 7 == 0 {"\n"} E ‘ ’)</syntaxhighlight>
{{out}}
<pre>
Quadrat special primes < 16000:
2 3 7 11 47 83 227
263 587 911 947 983 1019 1163
1307 1451 1487 1523 1559 2459 3359
4259 4583 5483 5519 5843 5879 6203
6779 7103 7247 7283 7607 7643 8219
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Action!}}==
{{libheader|Action! Sieve of Eratosthenes}}
<syntaxhighlight lang="action!">INCLUDE "H6:SIEVE.ACT"
DEFINE MAX="15999"
DEFINE MAXSQUARES="126"
BYTE ARRAY primes(MAX+1)
INT ARRAY squares(MAXSQUARES)
PROC CalcSquares()
INT i
FOR i=1 TO MAXSQUARES
DO
squares(i-1)=i*i
OD
RETURN
INT FUNC FindNextQuadraticPrime(INT x)
INT i,next
FOR i=0 TO MAXSQUARES-1
DO
next=x+squares(i)
IF next>MAX THEN
RETURN (-1)
FI
IF primes(next) THEN
RETURN (next)
FI
OD
RETURN (-1)
PROC Main()
INT p=[2]
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
CalcSquares()
WHILE p>0
DO
PrintI(p) Put(32)
p=FindNextQuadraticPrime(p)
OD
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Quadrat_Special_Primes.png Screenshot from Atari 8-bit computer]
<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459
3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363
10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|ALGOL 68}}==
{{Trans|ALGOL W}}
{{libheader|ALGOL 68-primes}}
<syntaxhighlight lang="algol68">BEGIN # find some primes where the gap between the current prime and the next is a square #
# an array of squares #
PROC get squares = ( INT n )[]INT:
Line 30 ⟶ 114:
END # get squares # ;
INT max number = 16000;
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE max number;
[]INT square = get squares( max number );
INT p count, this prime, next prime;
Line 47 ⟶ 132:
DO sq pos +:= 2 OD
OD
END</
{{out}}
<pre>
Line 58 ⟶ 143:
=={{header|ALGOL W}}==
<
% sets p( 1 :: n ) to a sieve of primes up to n %
procedure Eratosthenes ( logical array p( * ) ; integer value n ) ;
Line 100 ⟶ 185:
end while_thisPrime_lt_MAX_NUMBER
end
end.</
{{out}}
<pre>
Line 108 ⟶ 193:
10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771
15671
</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f QUADRAT_SPECIAL_PRIMES.AWK
# converted from FreeBASIC
BEGIN {
stop = 15999
p = 2
j = 1
printf("%5d ",p)
count++
while (1) {
while (1) {
if (is_prime(p+j*j)) { break }
j++
}
p += j*j
if (p > stop) { break }
printf("%5d%1s",p,++count%10?"":"\n")
j = 1
}
printf("\nQuadrat special primes 1-%d: %d\n",stop,count)
exit(0)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
</syntaxhighlight>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911
947 983 1019 1163 1307 1451 1487 1523 1559 2459
3359 4259 4583 5483 5519 5843 5879 6203 6779 7103
7247 7283 7607 7643 8219 8363 10667 11243 11279 11423
12323 12647 12791 13367 13691 14591 14627 14771 15671
Quadrat special primes 1-15999: 49
</pre>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
{{trans|BASIC256}}
<syntaxhighlight lang="gwbasic"> 100 FOR P = 2 TO 16000
110 PRINT S$P;
120 LET S$ = " "
130 FOR J = 1 TO 1E9
140 LET V = P + J * J
150 GOSUB 200"IS PRIME"
160 IF NOT ISPRIME THEN NEXT J
170 LET P = V - 1
180 NEXT P
190 END
200 DEF FN MOD(DIVISR) = V - INT (V / DIVISR) * DIVISR
210 ISPRIME = FALSE
220 IF V < 2 THEN RETURN
230 ISPRIME = V = 2
240 IF FN MOD(2) = 0 THEN RETURN
250 ISPRIME = V = 3
260 IF FN MOD(3) = 0 THEN RETURN
270 FOR D = 5 TO SQR (V) STEP 2
280 LET ISPRIME = FN MOD(D)
290 IF NOT ISPRIME THEN RETURN
300 NEXT D
310 RETURN</syntaxhighlight>
==={{header|BASIC256}}===
<syntaxhighlight lang="basic256">function isPrime(v)
if v < 2 then return False
if v mod 2 = 0 then return v = 2
if v mod 3 = 0 then return v = 3
d = 5
while d * d <= v
if v mod d = 0 then return False else d += 2
end while
return True
end function
p = 2
j = 1
print 2; " ";
while True
while True
if isPrime(p + j*j) then exit while
j += 1
end while
p += j*j
if p > 16000 then exit while
print p; " ";
j = 1
end while
end</syntaxhighlight>
==={{header|PureBasic}}===
<syntaxhighlight lang="purebasic">Procedure isPrime(v.i)
If v <= 1 : ProcedureReturn #False
ElseIf v < 4 : ProcedureReturn #True
ElseIf v % 2 = 0 : ProcedureReturn #False
ElseIf v < 9 : ProcedureReturn #True
ElseIf v % 3 = 0 : ProcedureReturn #False
Else
Protected r = Round(Sqr(v), #PB_Round_Down)
Protected f = 5
While f <= r
If v % f = 0 Or v % (f + 2) = 0
ProcedureReturn #False
EndIf
f + 6
Wend
EndIf
ProcedureReturn #True
EndProcedure
OpenConsole()
p.i = 2
j.i = 1
Print("2" + #TAB$)
Repeat
Repeat
If isPrime(p + j*j)
Break
EndIf
j + 1
ForEver
p + j*j
If p > 16000
Break
EndIf
Print(Str(p) + #TAB$)
j = 1
ForEver
Input()
CloseConsole()</syntaxhighlight>
==={{header|Yabasic}}===
<syntaxhighlight lang="yabasic">sub isPrime(v)
if v < 2 then return False : fi
if mod(v, 2) = 0 then return v = 2 : fi
if mod(v, 3) = 0 then return v = 3 : fi
d = 5
while d * d <= v
if mod(v, d) = 0 then return False else d = d + 2 : fi
wend
return True
end sub
p = 2
j = 1
print 2, " ";
do
do
if isPrime(p + j*j) then break : fi
j = j + 1
loop
p = p + j*j
if p > 16000 then break : fi
print p, " ";
j = 1
loop
end</syntaxhighlight>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N+0.0));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
procedure QuadratSpecialPrimes(Memo: TMemo);
var Q,P,Cnt: integer;
var IA: TIntegerDynArray;
begin
Memo.Lines.Add('Count Prime1 Prime2 Gap Sqrt');
Memo.Lines.Add('---------------------------------');
Cnt:=0;
Q:=2;
for P:=3 to 16000-1 do
if IsPrime(P) then
begin
if frac(sqrt(P - Q))=0 then
begin
Inc(Cnt);
Memo.Lines.Add(Format('%5D%7D%8D%7D%6.1f',[Cnt,Q,P,P-Q,Sqrt(P-Q)]));
Q:=P;
end;
end;
Memo.Lines.Add('Count = '+IntToStr(Cnt));
end;
</syntaxhighlight>
{{out}}
<pre>
Count Prime1 Prime2 Gap Sqrt
---------------------------------
1 2 3 1 1.0
2 3 7 4 2.0
3 7 11 4 2.0
4 11 47 36 6.0
5 47 83 36 6.0
6 83 227 144 12.0
7 227 263 36 6.0
8 263 587 324 18.0
9 587 911 324 18.0
10 911 947 36 6.0
11 947 983 36 6.0
12 983 1019 36 6.0
13 1019 1163 144 12.0
14 1163 1307 144 12.0
15 1307 1451 144 12.0
16 1451 1487 36 6.0
17 1487 1523 36 6.0
18 1523 1559 36 6.0
19 1559 2459 900 30.0
20 2459 3359 900 30.0
21 3359 4259 900 30.0
22 4259 4583 324 18.0
23 4583 5483 900 30.0
24 5483 5519 36 6.0
25 5519 5843 324 18.0
26 5843 5879 36 6.0
27 5879 6203 324 18.0
28 6203 6779 576 24.0
29 6779 7103 324 18.0
30 7103 7247 144 12.0
31 7247 7283 36 6.0
32 7283 7607 324 18.0
33 7607 7643 36 6.0
34 7643 8219 576 24.0
35 8219 8363 144 12.0
36 8363 10667 2304 48.0
37 10667 11243 576 24.0
38 11243 11279 36 6.0
39 11279 11423 144 12.0
40 11423 12323 900 30.0
41 12323 12647 324 18.0
42 12647 12791 144 12.0
43 12791 13367 576 24.0
44 13367 13691 324 18.0
45 13691 14591 900 30.0
46 14591 14627 36 6.0
47 14627 14771 144 12.0
48 14771 15671 900 30.0
Count = 48
Elapsed Time: 111.233 ms.
</pre>
=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]
<syntaxhighlight lang="fsharp">
//Quadrat special primes. Nigel Galloway: January 16th., 2023
let isPs(n:int)=MathNet.Numerics.Euclid.IsPerfectSquare n
let rec fG n g=seq{match Seq.tryHead g with Some h when isPs(h-n)->yield h; yield! fG h g |Some _->yield! fG n g |_->()}
fG 2 (primes32()|>Seq.takeWhile((>)16000))|>Seq.iter(printf "%d "); printfn ""
</syntaxhighlight>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Factor}}==
{{works with|Factor|0.98}}
<syntaxhighlight lang="factor">USING: fry io kernel lists lists.lazy math math.primes prettyprint ;
2 [ 1 lfrom swap '[ sq _ + ] lmap-lazy [ prime? ] lfilter car ]
lfrom-by [ 16000 < ] lwhile [ pprint bl ] leach nl</syntaxhighlight>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">
#include "isprime.bas"
dim as integer p = 2, j = 1
print 2;" ";
do
do
if isprime(p + j*j) then exit do
j += 1
loop
p += j*j
if p > 16000 then exit do
print p;" ";
j = 1
loop
print
</syntaxhighlight>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
local fn IsPrime( n as NSUInteger ) as BOOL
BOOL isPrime = YES
NSUInteger i
if n < 2 then exit fn = NO
if n = 2 then exit fn = YES
if n mod 2 == 0 then exit fn = NO
for i = 3 to int(n^.5) step 2
if n mod i == 0 then exit fn = NO
next
end fn = isPrime
local fn QuadratSpecialPrimes
NSUInteger p = 2, j = 1, count = 1
printf @"%6lu \b", 2
while (1)
count++
while (1)
if fn IsPrime( p + j*j ) then exit while
j += 1
wend
p += j*j
if p > 16000 then exit while
printf @"%6lu \b", p
if count == 7 then count = 0 : print
j = 1
wend
print
end fn
fn QuadratSpecialPrimes
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
2 3 7 11 47 83 227
263 587 911 947 983 1019 1163
1307 1451 1487 1523 1559 2459 3359
4259 4583 5483 5519 5843 5879 6203
6779 7103 7247 7283 7607 7643 8219
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Go}}==
{{trans|Wren}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
)
func sieve(limit int) []bool {
limit++
// True denotes composite, false denotes prime.
c := make([]bool, limit) // all false by default
c[0] = true
c[1] = true
// no need to bother with even numbers over 2 for this task
p := 3 // Start from 3.
for {
p2 := p * p
if p2 >= limit {
break
}
for i := p2; i < limit; i += 2 * p {
c[i] = true
}
for {
p += 2
if !c[p] {
break
}
}
}
return c
}
func isSquare(n int) bool {
s := int(math.Sqrt(float64(n)))
return s*s == n
}
func commas(n int) string {
s := fmt.Sprintf("%d", n)
if n < 0 {
s = s[1:]
}
le := len(s)
for i := le - 3; i >= 1; i -= 3 {
s = s[0:i] + "," + s[i:]
}
if n >= 0 {
return s
}
return "-" + s
}
func main() {
c := sieve(15999)
fmt.Println("Quadrat special primes under 16,000:")
fmt.Println(" Prime1 Prime2 Gap Sqrt")
lastQuadSpecial := 3
gap := 1
count := 1
fmt.Printf("%7d %7d %6d %4d\n", 2, 3, 1, 1)
for i := 5; i < 16000; i += 2 {
if c[i] {
continue
}
gap = i - lastQuadSpecial
if isSquare(gap) {
sqrt := int(math.Sqrt(float64(gap)))
fmt.Printf("%7s %7s %6s %4d\n", commas(lastQuadSpecial), commas(i), commas(gap), sqrt)
lastQuadSpecial = i
count++
}
}
fmt.Println("\n", count+1, "such primes found.")
}</syntaxhighlight>
{{out}}
<pre>
Same as Wren example.
</pre>
=={{header|J}}==
<syntaxhighlight lang="j">{{
j=. 0
r=. 2
while. (j=.j+1)<#y do.
if. (=<.)%:(j{y)-{:r do. r=. r, j{y end.
end.
}} p:i.p:inv 16e3
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671</syntaxhighlight>
=={{header|jq}}==
'''Adaptation of [[#Julia|Julia]]
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
For the definition of `is_prime` used here, see https://rosettacode.org/wiki/Additive_primes
<syntaxhighlight lang="jq">
# Input: a number > 2
# Output: an array of the quadrat primes less than `.`
def quadrat:
. as $N
| ($N|sqrt) as $lastn
| { qprimes: [2], q: 2 }
| until ( .qprimes[-1] >= $N or .q >= $N;
label $out
| foreach range(1; $lastn + 1) as $i (.;
.q = .qprimes[-1] + $i * $i
| if .q >= $N then .emit = true
elif .q|is_prime then .qprimes = .qprimes + [.q]
| .emit = true
else .
end;
select(.emit)) | {qprimes, q}, break $out )
| .qprimes ;
"Quadrat special primes < 16000:",
(16000 | quadrat[])
</syntaxhighlight>
{{out}}
<pre>
Quadrat special primes < 16000:
2
3
7
...
14627
14771
15671
</pre>
=={{header|Julia}}==
<
function quadrat(N = 16000)
Line 132 ⟶ 716:
println("Quadrat special primes < 16000:")
foreach(p -> print(rpad(p[2], 6), p[1] % 10 == 0 ? "\n" : ""), enumerate(quadrat()))
</
<pre>
Quadrat special primes < 16000:
Line 141 ⟶ 725:
12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Ksh}}==
<syntaxhighlight lang="ksh">
#!/bin/ksh
# Quadrat Special Primes
# # Variables:
#
alias SHORTINT='typeset -si'
SHORTINT MAXN=16000
# # Functions:
#
# # Function _isquadrat(n, m) return 1 when (m-n) is a perfect square
#
function _isquadrat {
typeset _n ; SHORTINT _n=$1
typeset _m ; SHORTINT _m=$2
[[ $(( sqrt(_m - _n) )) == +(\d).+(\d) ]] && return 0
return 1
}
# # Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
typeset _n ; integer _n=$1
typeset _i ; integer _i
(( _n < 2 )) && return 0
for (( _i=2 ; _i*_i<=_n ; _i++ )); do
(( ! ( _n % _i ) )) && return 0
done
return 1
}
######
# main #
######
SHORTINT i prev_pr=2
for ((i=2; i<MAXN; i++)); do
_isprime ${i}
if (( $? )); then
_isquadrat ${prev_pr} ${i}
if (( $? )); then
printf "%d " ${i}
prev_pr=${i}
fi
fi
done
printf "\n"
</syntaxhighlight>
{{out}}<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ps = {2};
Do[
Do[
q = Last[ps] + i^2;
If[PrimeQ[q],
AppendTo[ps, q];
Break[]
]
,
{i, 1, \[Infinity]}
];
If[Last[ps] >= 16000,
Break[]]
,
{\[Infinity]}
];
ps //= Most;
Multicolumn[ps, {Automatic, 7}, Appearance -> "Horizontal"]</syntaxhighlight>
{{out}}
<pre>2 3 7 11 47 83 227
263 587 911 947 983 1019 1163
1307 1451 1487 1523 1559 2459 3359
4259 4583 5483 5519 5843 5879 6203
6779 7103 7247 7283 7607 7643 8219
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
quadrat(n):=block(aux:next_prime(n),while not integerp(sqrt(aux-n)) do aux:next_prime(aux),aux)$
block(a:2,append([a],makelist(a:quadrat(a),48)));
</syntaxhighlight>
{{out}}
<pre>
[2,3,7,11,47,83,227,263,587,911,947,983,1019,1163,1307,1451,1487,1523,1559,2459,3359,4259,4583,5483,5519,5843,5879,6203,6779,7103,7247,7283,7607,7643,8219,8363,10667,11243,11279,11423,12323,12647,12791,13367,13691,14591,14627,14771,15671]
</pre>
=={{header|Nim}}==
<syntaxhighlight lang="nim">import math, strutils, sugar
func isPrime(n: Natural): bool =
if n < 2: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, 2
if n mod d == 0: return false
inc d, 4
result = true
const
Max = 16_000
Squares = collect(newSeq):
for n in countup(2, sqrt(Max.float).int, 2): n * n
iterator quadraPrimes(lim: Positive): int =
assert lim >= 3
yield 2
yield 3
var n = 3
block mainloop:
while true:
for square in Squares:
let next = n + square
if next > lim: break mainloop
if next.isPrime:
n = next
yield n
break
echo "Quadrat special primes < 16000:"
var count = 0
for qp in quadraPrimes(Max):
inc count
stdout.write ($qp).align(5), if count mod 7 == 0: '\n' else: ' '</syntaxhighlight>
{{out}}
<pre>Quadrat special primes < 16000:
2 3 7 11 47 83 227
263 587 911 947 983 1019 1163
1307 1451 1487 1523 1559 2459 3359
4259 4583 5483 5519 5843 5879 6203
6779 7103 7247 7283 7607 7643 8219
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
use ntheory 'is_prime';
my @sp = my $previous = 2;
do {
my($next,$n);
while () { last if is_prime( $next = $previous + ++$n**2 ) }
push @sp, $next;
$previous = $next;
} until $sp[-1] >= 16000;
pop @sp and say ((sprintf '%-7d'x@sp, @sp) =~ s/.{1,$#sp}\K\s/\n/gr);</syntaxhighlight>
{{out}}
<pre>2 3 7 11 47 83 227
263 587 911 947 983 1019 1163
1307 1451 1487 1523 1559 2459 3359
4259 4583 5483 5519 5843 5879 6203
6779 7103 7247 7283 7607 7643 8219
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671</pre>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">constant</span> <span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"linear quadratic cubic quartic quintic sextic septic octic nonic decic"</span><span style="color: #0000FF;">),</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">p</span><span style="color: #
<span style="color: #004080;">
<span style="color: #
<span style="color: #004080;">bool</span> <span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">while</span> <span style="color: #008080;">not</span> <span style="color: #000000;">done</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lastn</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">
<span style="color: #008080;">if</span> <span style="color: #000000;">
<span style="color: #
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">is_prime</span><span style="color: #
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">m</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #008000;">"%,6d"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">res</span><span style="color: #0000FF;">}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Found 49
2 3 7 11 47 83 227
263 587 911 947 983 1,019 1,163
Line 174 ⟶ 932:
8,363 10,667 11,243 11,279 11,423 12,323 12,647
12,791 13,367 13,691 14,591 14,627 14,771 15,671
Found 23 cubic special primes < 15000:
2 3 11 19 83 1,811 2,027 2,243
2,251 2,467 2,531 2,539 3,539 3,547 4,547 5,059
10,891 12,619 13,619 13,627 13,691 13,907 14,419
Found 9 quartic special primes < 1.4e+10:
2 3 19 160,019 1,049,920,019 1,050,730,019 1,051,540,019 12,910,750,019 13,960,510,019
Found 9 quintic special primes < 8.025e+8:
2 3 32,771 32,803 33,827 41,603 579,427 778,179,427 802,479,427
Found 6 sextic special primes < 2.5e+13:
2 3 67 131 2,176,782,467 22,485,250,805,891
Found 7 septic special primes < 1.95e+14:
2 3 131 194,871,710,000,131 194,893,580,000,131 194,893,580,280,067 194,971,944,444,163
Found 4 octic special primes < 7.5e+12:
2 3 65,539 6,553,600,065,539
Found 6 nonic special primes < 3e+9:
2 3 262,147 10,339,843 20,417,539 1,020,417,539
Found 4 decic special primes < 1.1e+9:
2 3 1,073,741,827 1,073,742,851
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">#!/usr/bin/python
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
if __name__ == '__main__':
p = 2
j = 1
print(2, end = " ");
while True:
while True:
if isPrime(p + j*j):
break
j += 1
p += j*j
if p > 16000:
break
print(p, end = " ");
j = 1</syntaxhighlight>
=={{header|Raku}}==
<syntaxhighlight lang="raku"
my $next;
for (1..∞).map: *² {
Line 188 ⟶ 998:
say "{+$_} matching numbers:\n", $_».fmt('%5d').batch(7).join: "\n" given
@sqp[^(@sqp.first: * > 16000, :k)];</
{{out}}
<pre>49 matching numbers:
Line 200 ⟶ 1,010:
=={{header|REXX}}==
<
/*─────────────────────────────────────────────────── are the smallest quadrat numbers. */
parse arg hi cols . /*obtain optional argument from the CL.*/
Line 207 ⟶ 1,017:
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
'difference of successive
if cols>0 then say ' index │'center(
if cols>0 then say '───────┼'center(""
sqp= 0;
op= 1
$= /*
do j=0 by 0
do k=1 until !.np; np= op + k*k /*find the next square + oldPrime.*/
Line 220 ⟶ 1,030:
sqp= sqp + 1 /*bump the number of sqp's. */
op= np /*assign the newPrime to the oldPrime*/
if cols
c= commas(np) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add
if sqp//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
Line 229 ⟶ 1,039:
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found '
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Line 244 ⟶ 1,055:
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</
{{out|output|text= when using the default inputs:}}
<pre>
Line 259 ⟶ 1,069:
31 │ 7,247 7,283 7,607 7,643 8,219 8,363 10,667 11,243 11,279 11,423
41 │ 12,323 12,647 12,791 13,367 13,691 14,591 14,627 14,771 15,671
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────
Found 49 of the smallest primes < 16,000 such that the difference of successive terma are the smallest quadrat numbers
Line 264 ⟶ 1,075:
=={{header|Ring}}==
<syntaxhighlight lang="ring">load "stdlib.ring"
/* Searching for the smallest prime gaps under a limit,
such that the difference of successive terms (gaps)
is of the smallest degree. */
desc = split("na quadratic cubic quartic quintic sextic septic octic nonic decic"," ")
limits = [1, 16000, 15000, 30000, 50000, 50000, 50000, 75000, 300000, 500000]
for deg = 2 to len(desc)
Primes = []
limit = limits[deg]
oldPrime = 2
add(Primes,
for n =
nextPrime = oldPrime + pow(n, deg)
if nextPrime < limit add(Primes, nextPrime) ok
oldPrime = nextPrime
else
nextPrime = nextPrime - oldPrime
ok
if nextPrime > limit exit ok
next
? nl + desc[deg] + ":" + nl + " prime1 prime2 Gap Rt"
for n = 1 to Len(Primes) - 1
diff = Primes[n + 1] - Primes[n]
? sf(Primes[n], 7) + " " + sf(Primes[n+1], 7) + " " + sf(diff, 6) + " " + sf(floor(0.49 + pow(diff, 1 / deg)), 4)
next
? "Found " + Len(Primes) + " primes under " + limit + " for " + desc[deg] + " gaps."
next
? nl + "done..."
# a very plain string formatter, intended to even up columnar outputs
def sf x, y
s = string(x) l = len(s)
if l > y y = l ok
return substr(" ", 11 - y + l) + s</syntaxhighlight>
{{out}}
<pre style="height:20em">working...
quadratic:
prime1 prime2 Gap Rt
2 3 1 1
3 7 4 2
7 11 4 2
11 47 36 6
47 83 36 6
83 227 144 12
227 263 36 6
263 587 324 18
587 911 324 18
911 947 36 6
947 983 36 6
983 1019 36 6
1019 1163 144 12
1163 1307 144 12
1307 1451 144 12
1451 1487 36 6
1487 1523 36 6
1523 1559 36 6
1559 2459 900 30
2459 3359 900 30
3359 4259 900 30
4259 4583 324 18
4583 5483 900 30
5483 5519 36 6
5519 5843 324 18
5843 5879 36 6
5879 6203 324 18
6203 6779 576 24
6779 7103 324 18
7103 7247 144 12
7247 7283 36 6
7283 7607 324 18
7607 7643 36 6
7643 8219 576 24
8219 8363 144 12
8363 10667 2304 48
10667 11243 576 24
11243 11279 36 6
11279 11423 144 12
11423 12323 900 30
12323 12647 324 18
12647 12791 144 12
12791 13367 576 24
13367 13691 324 18
13691 14591 900 30
14591 14627 36 6
14627 14771 144 12
14771 15671 900 30
Found 49 primes under 16000 for quadratic gaps.
cubic:
prime1 prime2 Gap Rt
2 3 1 1
3 11 8 2
11 19 8 2
19 83 64 4
83 1811 1728 12
1811 2027 216 6
2027 2243 216 6
2243 2251 8 2
2251 2467 216 6
2467 2531 64 4
2531 2539 8 2
2539 3539 1000 10
3539 3547 8 2
3547 4547 1000 10
4547 5059 512 8
5059 10891 5832 18
10891 12619 1728 12
12619 13619 1000 10
13619 13627 8 2
13627 13691 64 4
13691 13907 216 6
13907 14419 512 8
Found 23 primes under 15000 for cubic gaps.
quartic:
prime1 prime2 Gap Rt
2 3 1 1
3 19 16 2
Found 3 primes under 30000 for quartic gaps.
quintic:
prime1 prime2 Gap Rt
2 3 1 1
3 32771 32768 8
32771 32803 32 2
32803 33827 1024 4
33827 41603 7776 6
Found 6 primes under 50000 for quintic gaps.
sextic:
prime1 prime2 Gap Rt
2 3 1 1
3 67 64 2
67 131 64 2
Found 4 primes under 50000 for sextic gaps.
septic:
prime1 prime2 Gap Rt
2 3 1 1
3 131 128 2
Found 3 primes under 50000 for septic gaps.
octic:
prime1 prime2 Gap Rt
2 3 1 1
3 65539 65536 4
Found 3 primes under 75000 for octic gaps.
nonic:
prime1 prime2 Gap Rt
2 3 1 1
3 262147 262144 4
Found 3 primes under 300000 for nonic gaps.
decic:
prime1 prime2 Gap Rt
2 3 1 1
Found 2 primes under 500000 for decic gaps.
done...</pre>
=={{header|RPL}}==
{{works with|HP|49}}
≪ <span style="color:red">{ 2 } 2</span> DUP
'''DO'''
DUP NEXTPRIME
'''IF''' DUP2 SWAP - √ FP NOT '''THEN''' NIP SWAP OVER + SWAP DUP '''END'''
'''UNTIL''' DUP <span style="color:red">16000</span> ≥ '''END'''
DROP2
≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: {2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671}
</pre>
Runs in 6 minutes 25 seconds on a HP-50g.
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
res = [2]
until res.last > 16000 do
res << (1..).detect{|n| (res.last + n**2).prime? } ** 2 + res.last
end
puts res[..-2].join(" ")
</syntaxhighlight>
{{out}}
<pre>2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func quadrat_primes(callback) {
var prev = 2
callback(prev)
loop {
var curr = (1..Inf -> lazy.map { prev + _**2 }.first { .is_prime })
callback(curr)
prev = curr
}
}
say gather {
quadrat_primes({|k|
break if (k >= 16000)
take(k)
})
}</syntaxhighlight>
{{out}}
<pre>
[2, 3, 7, 11, 47, 83, 227, 263, 587, 911, 947, 983, 1019, 1163, 1307, 1451, 1487, 1523, 1559, 2459, 3359, 4259, 4583, 5483, 5519, 5843, 5879, 6203, 6779, 7103, 7247, 7283, 7607, 7643, 8219, 8363, 10667, 11243, 11279, 11423, 12323, 12647, 12791, 13367, 13691, 14591, 14627, 14771, 15671]
</pre>
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./math" for Int
import "./fmt" for Fmt
var isSquare = Fn.new { |n|
var s = n.sqrt.floor
return s*s == n
}
var primes = Int.primeSieve(15999)
System.print("Quadrat special primes under 16,000:")
System.print(" Prime1 Prime2 Gap Sqrt")
var lastQuadSpecial = 3
var gap = 1
var count = 1
Fmt.print("$,7d $,7d $,6d $4d", 2, 3, 1, 1)
for (p in primes.skip(2)) {
gap = p - lastQuadSpecial
if (isSquare.call(gap)) {
Fmt.print("$,7d $,7d $,6d $4d", lastQuadSpecial, p, gap, gap.sqrt)
lastQuadSpecial = p
count = count + 1
}
}
System.print("\n%(count+1) such primes found.")</syntaxhighlight>
{{out}}
<pre>
Quadrat special primes under 16,000:
Prime1 Prime2 Gap Sqrt
2 3 1 1
3 7 4 2
7 11 4 2
11 47 36 6
47 83 36 6
83 227 144 12
227 263 36 6
263 587 324 18
587 911 324 18
911 947 36 6
947 983 36 6
983 1,019 36 6
1,019 1,163 144 12
1,163 1,307 144 12
1,307 1,451 144 12
1,451 1,487 36 6
1,487 1,523 36 6
1,523 1,559 36 6
1,559 2,459 900 30
2,459 3,359 900 30
3,359 4,259 900 30
4,259 4,583 324 18
4,583 5,483 900 30
5,483 5,519 36 6
5,519 5,843 324 18
5,843 5,879 36 6
5,879 6,203 324 18
6,203 6,779 576 24
6,779 7,103 324 18
7,103 7,247 144 12
7,247 7,283 36 6
7,283 7,607 324 18
7,607 7,643 36 6
7,643 8,219 576 24
8,219 8,363 144 12
8,363 10,667 2,304 48
10,667 11,243 576 24
11,243 11,279 36 6
11,279 11,423 144 12
11,423 12,323 900 30
12,323 12,647 324 18
12,647 12,791 144 12
12,791 13,367 576 24
13,367 13,691 324 18
13,691 14,591 900 30
14,591 14,627 36 6
14,627 14,771 144 12
14,771 15,671 900 30
49 such primes found.
</pre>
=={{header|XPL0}}==
Find primes where the difference between the current one and a following one is a perfect square.
<syntaxhighlight lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true;
];
int Count, P, Q;
[Count:= 0;
P:= 2; Q:= 3;
repeat if IsPrime(Q) then
[if sq(sqrt(Q-P)) = Q-P then
[IntOut(0, P);
P:= Q;
Count:= Count+1;
if rem(Count/10) then ChOut(0, 9\tab\) else CrLf(0);
];
];
Q:= Q+2;
until P >= 16000;
CrLf(0);
IntOut(0, Count);
Text(0, " such primes found below 16000.
");
]</syntaxhighlight>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911
947 983 1019 1163 1307 1451 1487 1523 1559 2459
3359 4259 4583 5483 5519 5843 5879 6203 6779 7103
7247 7283 7607 7643 8219 8363 10667 11243 11279 11423
12323 12647 12791 13367 13691 14591 14627 14771 15671
49 such primes found below 16000.
</pre>
| |||