Next special primes: Difference between revisions
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where '''n''' < '''1050'''.
<br><br>
=={{header|11l}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="11l">F is_prime(a)
I a == 2
R 1B
I a < 2 | a % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(a))).step(2)
I a % i == 0
R 0B
R 1B
V p = 3
V i = 2
print(‘2 3’, end' ‘ ’)
L p + i < 1050
I is_prime(p + i)
p += i
print(p, end' ‘ ’)
i += 2</syntaxhighlight>
{{out}}
<pre>
2 3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049
</pre>
=={{header|Action!}}==
{{libheader|Action! Sieve of Eratosthenes}}
<syntaxhighlight lang="action!">INCLUDE "H6:SIEVE.ACT"
PROC Main()
DEFINE MAX="1049"
BYTE ARRAY primes(MAX+1)
INT i,count=[1],lastprime=[3],lastgap=[1]
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
PrintI(lastprime)
FOR i=1 TO MAX
DO
IF primes(i)=1 AND i-lastprime>lastgap THEN
lastgap=i-lastprime
lastprime=i
Put(32) PrintI(i)
count==+1
FI
OD
PrintF("%E%EThere are %I next special primes",count)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Next_special_primes.png Screenshot from Atari 8-bit computer]
<pre>
3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049
There are 26 next special primes
</pre>
=={{header|ALGOL W}}==
<
% the gap between previus primes and the current %
% sets p( 1 :: n ) to a sieve of primes up to n %
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end while_thisPrime_lt_MAX_NUMBER
end
end.</
{{out}}
<pre>
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26: 967 1049 82
</pre>
=={{header|Arturo}}==
<
lim: 1050
lastP: 3
lastGap: 1
loop 5.. .step:2 lim 'n [
if not? prime? n -> continue
if lastGap < n - lastP [
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print "List of next special primes less than 1050:"
print specials</
{{out}}
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=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f NEXT_SPECIAL_PRIMES.AWK
BEGIN {
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return(1)
}
</syntaxhighlight>
{{out}}
<pre>
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Next special primes 1-1050: 26
</pre>
=={{header|BASIC}}==
==={{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 = 3
i = 2
print "2 3 "; #special case
do
if isPrime(p + i) then
p += i
print p; " ";
end if
i += 2
until p + i >= 1050
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 = 3
i.i = 2
Print("2 3 ") ;special Case
Repeat
If isPrime(p + i)
p + i
Print(Str(p) + " ")
EndIf
i + 2
Until p + i >= 1050
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 = 3
i = 2
print "2 3 "; //special case
repeat
if isPrime(p + i) = 1 then
p = p + i
print p;
endif
i = i + 2
until p + i >= 1050
end</syntaxhighlight>
=={{header|C}}==
<
#include <stdbool.h>
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}
}
}</
{{out}}
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=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]
<
// Next special primes. Nigel Galloway: March 26th., 2021
let mP=let mutable n,g=2,0 in primes32()|>Seq.choose(fun y->match y-n>g,n with (true,i)->g<-y-n; n<-y; Some(i,g,y) |_->None)
mP|>Seq.takeWhile(fun(_,_,n)->n<1050)|>Seq.iteri(fun i (n,g,l)->printfn "n%d=%d n%d=%d n%d-n%d=%d" i n (i+1) l (i+1) i g)
</syntaxhighlight>
{{out}}
<pre>
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Here's another way of writing the mP sequence above which is (hopefully) a little clearer:
<
let mP = seq {
let mutable prevp, maxdiff = 2, 0
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prevp <- p
}
</syntaxhighlight>
=={{header|Factor}}==
{{works with|Factor|0.98}}
<syntaxhighlight lang="text">USING: formatting io kernel math math.primes ;
"2 " write 1 3
[ dup 1050 < ] [
2dup "(%d) %d " printf [ + next-prime ] keep 2dup - nip swap
] while 2drop nl</
{{out}}
<pre>
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=={{header|FreeBASIC}}==
<
dim as integer p = 3, i = 2
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end if
i += 2
loop until p+i >=1050 : print</
{{out}}<pre>2 3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049</pre>
=={{header|Go}}==
<
import "fmt"
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}
}
}</
{{out}}
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967 1049 82
</pre>
=={{header|J}}==
<syntaxhighlight lang="j"> (, 4 p: (-~ +:)/@(_2&{.))^:(1049 > {:)^:_ (2 3)
2 3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049</syntaxhighlight>
=={{header|Java}}==
{{trans|C}}
<
private static boolean isPrime(int n) {
if (n < 2) return false;
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}
}
}</
{{out}}
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967 1049 82
</pre>
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
This entry uses `is_primes` as can be defined as in [[Erd%C5%91s-primes#jq]].
<syntaxhighlight lang="jq">
def primes:
2, (range(3;infinite;2) | select(is_prime));
def emit_until(cond; stream): label $out | stream | if cond then break $out else . end;
def special_primes:
foreach primes as $p ({};
.emit = null
| if .p == null then .p = $p | .emit = .p
else ($p - .p) as $g
| if $g > .gap then .p = $p | .gap=$g | .emit = .p
else .
end
end;
select(.emit).emit);
# The task
# The following assumesg invocation with the -n option:
emit_until(. >= 1050; special_primes)</syntaxhighlight>
{{out}}
Invocation example: jq -n -f program.jq
<pre>
2
3
5
11
19
29
41
59
79
101
127
157
191
227
269
313
359
409
461
521
587
659
733
809
887
967
1049
</pre>
=={{header|Julia}}==
<
let
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end
end
</
<pre>
Special primes under 1050:
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967 1049 82
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">max = 1050;
n = {2, 3};
Do[
If[PrimeQ[i],
lastdiff = n[[-1]] - n[[-2]];
If[i - n[[-1]] > lastdiff,
AppendTo[n, i]
]
]
,
{i, Max[n] + 1, max}
]
n</syntaxhighlight>
{{out}}
<pre>{2, 3, 5, 11, 19, 29, 41, 59, 79, 101, 127, 157, 191, 227, 269, 313, 359, 409, 461, 521, 587, 659, 733, 809, 887, 967, 1049}</pre>
=={{header|Nim}}==
<
func isPrime(n: Positive): bool =
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let list = collect(newSeq, for p in nextSpecialPrimes(1050): p)
echo "List of next special primes less than 1050:"
echo list.join(" ")</
{{out}}
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just showing the small difference to increasing prime gaps.<BR>LastPrime is updated outside or inside If
<
program NextSpecialprimes;
//increasing prime gaps see
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writeln;
NextSpecial;
end.</
{{out}}
<pre>
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=={{header|Perl}}==
{{libheader|ntheory}}
<
use warnings;
use feature <state say>;
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pop @specials;
printf "%4d %4d\n", @$_ for @specials;</
{{out}}
<pre> 2 0
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=={{header|Phix}}==
<!--<
<span style="color: #004080;">integer</span> <span style="color: #000000;">lastSpecial</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">lastGap</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Special primes under 1,050:\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</
{{out}}
<pre>
Line 736 ⟶ 963:
967 1049 82
</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 = 3
i = 2
print("2 3", end = " ");
while True:
if isPrime(p + i) == 1:
p += i
print(p, end = " ");
i += 2
if p + i >= 1050:
break</syntaxhighlight>
=={{header|Quackery}}==
<code>isprime</code> is defined at [[Primality by trial division#Quackery]].
<syntaxhighlight lang="Quackery"> ' [ 2 ] 1
[ over -1 peek +
[ dup isprime
not while
1+ again ]
dup 1050 < while
join
dup -2 split nip
do swap - 1+ again ]
drop
echo
</syntaxhighlight>
{{out}}
<pre>[ 2 3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049 ]</pre>
=={{header|Raku}}==
<syntaxhighlight lang="raku"
state @primes = grep *.is-prime, 2..*;
shift @primes while @primes[0] <= $previous + $gap;
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my $limit = @specials.first: :k, *.[0] > 1050;
say .fmt('%4d') for @specials.head($limit);</
{{out}}
<pre>
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=={{header|REXX}}==
{{trans|RING}}
<
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 1050 /* " " " " " " */
Line 817 ⟶ 1,089:
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5;
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 to hi /*find odd primes from here on. */
parse var j '' -1 _;
if j//3==0 then
do k=5 while sq.k<=j
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j;
end /*j*/; return</
{{out|output|text= when using the default inputs:}}
<pre>
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=={{header|Ring}}==
<
load "stdlib.ring"
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see nl + "done..." + nl
</syntaxhighlight>
{{out}}
<pre>
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967 1049 82
done...
</pre>
=={{header|RPL}}==
≪ 0 → gap
≪ {2} 2 1 CF
'''WHILE''' 1 FC? '''REPEAT'''
DUP
'''DO''' NEXTPRIME '''UNTIL''' DUP2 - gap < '''END'''
'''IF''' DUP 1050 < '''THEN'''
DUP2 - 'gap' STO
NIP SWAP OVER + SWAP
'''ELSE''' 1 SF '''END'''
'''END''' DROP2
≫ ≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: {2 3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049}
</pre>
=={{header|Sidef}}==
<
var gap = 0
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special_primes(1050).each_2d {|p,gap|
say "#{'%4s' % p} #{'%4s' % gap}"
}</
{{out}}
<pre>
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{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<
import "./fmt" for Fmt
var primes = Int.primeSieve(1049)
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lastSpecial = p
}
}</
{{out}}
<pre>
Special primes under 1,050:
Prime1 Prime2 Gap
2 3 1
3 5 2
5 11 6
11 19 8
19 29 10
29 41 12
41 59 18
59 79 20
79 101 22
101 127 26
127 157 30
157 191 34
191 227 36
227 269 42
269 313 44
313 359 46
359 409 50
409 461 52
461 521 60
521 587 66
587 659 72
659 733 74
733 809 76
809 887 78
887 967 80
967 1049 82
</pre>
=={{header|XPL0}}==
{{trans|C}}
<syntaxhighlight lang "XPL0">include xpllib; \for IsPrime and Print
int I, LastSpecial, LastGap;
[LastSpecial:= 3; LastGap:= 1;
Print("Special primes under 1,050:\n");
Print("Prime1 Prime2 Gap\n");
Print("%6d %6d %3d\n", 2, 3, LastGap);
for I:= 5 to 1050-1 do
[if IsPrime(I) and I-LastSpecial > LastGap then
[LastGap:= I - LastSpecial;
Print("%6d %6d %3d\n", LastSpecial, I, LastGap);
LastSpecial:= I;
];
I:= I+1;
];
]</syntaxhighlight>
{{out}}
<pre>
| |||