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Prime numbers p for which the sum of primes less than or equal to p is prime (view source)

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{{Draft task}}
 
;Task:
;Task:Find prime numbers '''p''' which sum of prime numbers less or equal to '''p''' is prime, where '''p < 1000'''
Find primes &nbsp; '''p''' &nbsp; for which the sum of primes less than or equal to &nbsp; '''p''' &nbsp; is prime, &nbsp; where &nbsp; '''p &nbsp;&lt;&nbsp; 1,000'''.
 
<br><br>
 
=={{header|ALGOL 68}}==
Same as the [[Summarize primes#ALGOL_68]] solution.
<syntaxhighlight lang="algol68">BEGIN # sum the primes below n and report the sums that are prime #
INT max prime = 999; # largest prime to consider #
# sieve the primes to max prime #
[ 1 : max prime ]BOOL prime;
prime[ 1 ] := FALSE; prime[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( max prime ) DO
IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI
OD;
# sum the primes and test the sum #
INT prime sum := 0;
INT prime count := 0;
INT prime sum count := 0;
print( ( "prime prime", newline ) );
print( ( "count prime sum", newline ) );
FOR i TO max prime DO
IF prime[ i ] THEN
# have another prime #
prime count +:= 1;
prime sum +:= i;
# check whether the prime sum is prime or not #
BOOL is prime := TRUE;
FOR p TO i OVER 2 WHILE is prime DO
IF prime[ p ] THEN is prime := prime sum MOD p /= 0 FI
OD;
IF is prime THEN
# the prime sum is also prime #
prime sum count +:= 1;
print( ( whole( prime count, -5 )
, " "
, whole( i, -6 )
, " "
, whole( prime sum, -6 )
, newline
)
)
FI
FI
OD;
print( ( newline
, "Found "
, whole( prime sum count, 0 )
, " prime sums of primes below "
, whole( max prime + 1, 0 )
, newline
)
)
END</syntaxhighlight>
{{out}}
<pre>
prime prime
count prime sum
1 2 2
2 3 5
4 7 17
6 13 41
12 37 197
14 43 281
60 281 7699
64 311 8893
96 503 22039
100 541 24133
102 557 25237
108 593 28697
114 619 32353
122 673 37561
124 683 38921
130 733 43201
132 743 44683
146 839 55837
152 881 61027
158 929 66463
162 953 70241
 
Found 21 prime sums of primes below 1000
</pre>
=={{header|Arturo}}==
 
<syntaxhighlight lang="arturo">primes: select 1..1000 => prime?
 
pprimes: select primes 'x ->
prime? sum select primes 'y -> y =< x
 
loop split.every:7 pprimes 'x ->
print map x 's -> pad to :string s 4</syntaxhighlight>
 
{{out}}
 
<pre> 2 3 7 13 37 43 281
311 503 541 557 593 619 673
683 733 743 839 881 929 953</pre>
 
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f PRIME_NUMBERS_P_WHICH_SUM_OF_PRIME_NUMBERS_LESS_OR_EQUAL_TO_P_IS_PRIME.AWK
BEGIN {
start = 1
stop = 999
for (i=start; i<=stop; i++) {
if (is_prime(i)) {
sum += i
if (is_prime(sum)) {
printf("%4d%1s",i,++count%10?"":"\n")
}
}
}
printf("\n%d-%d: %d\n",start,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 13 37 43 281 311 503 541
557 593 619 673 683 733 743 839 881 929
953
1-999: 21
</pre>
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
 
 
<syntaxhighlight lang="Delphi">
procedure ShowPrimeLesserSum(Memo: TMemo);
var N,Sum,Cnt: integer;
var S: string;
begin
Cnt:=0;
Sum:=0;
for N:=2 to 1000-1 do
if IsPrime(N) then
begin
Sum:=Sum+N;
if IsPrime(Sum) then
begin
Inc(Cnt);
S:=S+Format('%4d',[N]);
If (Cnt mod 5)=0 then S:=S+CRLF;
end;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('Count='+IntToStr(Cnt));
end;
 
 
</syntaxhighlight>
{{out}}
<pre>
2 3 7 13 37
43 281 311 503 541
557 593 619 673 683
733 743 839 881 929
953
Count=21
Elapsed Time: 2.006 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">
// Primes (+)2..p is prime. Nigel Galloway: July 7th., 2021
primes32()|>Seq.takeWhile((>)1000)|>Seq.scan(fun(n,_) g->(n+g,g))(0,0)|>Seq.filter(fun(n,_)->isPrime n)|>Seq.iter(fun(_,n)->printf "%d " n); printfn ""
</syntaxhighlight>
=={{header|Factor}}==
{{works with|Factor|0.99 2021-06-02}}
<syntaxhighlight lang="factor">USING: assocs assocs.extras kernel math.primes math.statistics
prettyprint ;
 
1000 primes-upto dup cum-sum zip [ prime? ] filter-values .</syntaxhighlight>
{{out}}
<pre>
{
{ 2 2 }
{ 3 5 }
{ 7 17 }
{ 13 41 }
{ 37 197 }
{ 43 281 }
{ 281 7699 }
{ 311 8893 }
{ 503 22039 }
{ 541 24133 }
{ 557 25237 }
{ 593 28697 }
{ 619 32353 }
{ 673 37561 }
{ 683 38921 }
{ 733 43201 }
{ 743 44683 }
{ 839 55837 }
{ 881 61027 }
{ 929 66463 }
{ 953 70241 }
}
</pre>
 
 
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">
Dim As Integer column = 0, sum = 0, limit = 1000
 
Color 10 : Print !"N£meros primos 'p' menores de"; limit; _
!"\ncuya suma de todos los n£meros "; _
!"\nprimos <= p tambi‚n es primo:\n" : Color 7
 
For n As Integer = 1 To limit
If isprime(n) Then
sum += n
If isPrime(sum) Then
Print Using " ###"; n;
column += 1
If column Mod 7 = 0 Then Print : End If
End If
End If
Next n
 
Color 10 : Print !"\n\nEncontrados "; column; " n£meros."
Sleep
</syntaxhighlight>
{{out}}
<pre>
Números primos 'p' menores de 1000
cuya suma de todos los números
primos <= p también es primo:
 
2 3 7 13 37 43 281
311 503 541 557 593 619 673
683 733 743 839 881 929 953
 
Encontrados 21 números.
</pre>
 
=={{header|Go}}==
{{trans|Wren}}
<syntaxhighlight lang="go">package main
 
import (
"fmt"
"rcu"
)
 
func main() {
primes := rcu.Primes(1000)
maxSum := 0
for _, p := range primes {
maxSum += p
}
c := rcu.PrimeSieve(maxSum, true)
primeSum := 0
var results []int
for _, p := range primes {
primeSum += p
if !c[primeSum] {
results = append(results, p)
}
}
fmt.Println("Primes 'p' under 1000 where the sum of all primes <= p is also prime:")
for i, p := range results {
fmt.Printf("%4d ", p)
if (i+1)%7 == 0 {
fmt.Println()
}
}
fmt.Println("\nFound", len(results), "such primes")
}</syntaxhighlight>
 
{{out}}
<pre>
Primes 'p' under 1000 where the sum of all primes <= p is also prime:
2 3 7 13 37 43 281
311 503 541 557 593 619 673
683 733 743 839 881 929 953
 
Found 21 such primes
</pre>
 
=={{header|J}}==
<syntaxhighlight lang="j">(#~ 1 p: +/\)@(i.&.(p:^:_1)) 1000</syntaxhighlight>
{{out}}
<pre>2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953</pre>
 
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
 
This entry adopts the straightforward approach as used for example in the [[#awk|awk]] entry.
The jq implementation of this approach also turns out to be significantly faster than the jq implementation of the approach used in the [[#Wren|Wren]] entry.
 
See [[Erdős-primes#jq]] for a suitable definition of `is_prime` as
used here.
 
<syntaxhighlight lang="jq">def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
 
# Output: a stream of primes in range(0;$n)
def primes($n):
2, (range(3;$n;2) | select(is_prime));
 
# Output: a stream of primes satisfying the condition
def results($n):
foreach primes($n) as $p (0;
. + $p;
select(is_prime) | $p );
 
def task($n):
"Primes 'p' under \($n) for which the sum of primes <= p is also prime:",
( [results($n)]
| (_nwise(7) | map(lpad(4)) | join(" ")),
"\nFound \(length) such primes." );
 
task(1000)</syntaxhighlight>
{{out}}
<pre>
Primes 'p' under 1000 for which the sum of primes <= p is also prime:
2 3 7 13 37 43 281
311 503 541 557 593 619 673
683 733 743 839 881 929 953
 
Found 21 such primes.
</pre>
 
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Primes
 
primesumto(N) = begin s = 0; [i => s for i in 1:N if isprime(i) && isprime(s += i)] end
 
const primesumdict = primesumto(1000)
 
println("Prime Prime Sum to Prime\n---------------------------")
for p in primesumdict
println(rpad(p[1], 7), p[2])
end
println("\nTotal such primes < 1000: ", length(primesumdict))
</syntaxhighlight>{{out}}
<pre>
Prime Prime Sum to Prime
---------------------------
2 2
3 5
7 17
13 41
37 197
43 281
281 7699
311 8893
503 22039
541 24133
557 25237
593 28697
619 32353
673 37561
683 38921
733 43201
743 44683
839 55837
881 61027
929 66463
953 70241
 
Total such primes < 1000: 21
</pre>
 
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">cands = Most@NestWhileList[NextPrime, 2, # < 1000 &];
Partition[
cands[[Flatten@Position[PrimeQ /@ Accumulate[cands], True]]],
UpTo[5]] // TableForm</syntaxhighlight>
 
{{out}}<pre>
2 3 7 13 37
43 281 311 503 541
557 593 619 673 683
733 743 839 881 929
953
</pre>
 
=={{header|MiniScript}}==
<syntaxhighlight lang="miniscript">
isPrime = function(n)
if n <= 3 then return n > 1
if n % 2 == 0 or n % 3 == 0 then return false
i = 5
while i ^ 2 <= n
if n % i == 0 or n % (i + 2) == 0 then return false
i += 6
end while
return true
end function
 
primes = []
sum = 0
for n in range(2, 1000)
if isPrime(n) then
sum += n
if isPrime(sum) then primes.push(n)
end if
end for
print primes.len + " found: " + primes
</syntaxhighlight>
 
 
{{out}}
<pre>
21 found: [2, 3, 7, 13, 37, 43, 281, 311, 503, 541, 557, 593, 619, 673, 683, 733, 743, 839, 881, 929, 953</pre>
 
=={{header|Nim}}==
<syntaxhighlight lang="nim">import strutils, sugar
 
const
N = 1000 - 1 # Maximum value for prime.
S = N * (N + 1) div 2 # Maximum value for sum.
 
var composite: array[2..S, bool]
for n in 2..S:
let n2 = n * n
if n2 > S: break
if not composite[n]:
for k in countup(n2, S, n):
composite[k] = true
 
template isPrime(n: int): bool = not composite[n]
 
let primes = collect:
for n in 2..N:
if n.isPrime: n
 
var list: seq[int]
var sum = 0
for p in primes:
sum += p
if sum.isPrime:
list.add p
 
echo "Found $# primes:".format(list.len)
echo list.join(" ")</syntaxhighlight>
 
{{out}}
<pre>Found 21 primes:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953</pre>
 
=={{header|Perl}}==
<syntaxhighlight lang="perl">#!/usr/bin/perl
 
use strict; # https://rosettacode.org/wiki/Prime_numbers_p_which_sum_of_prime_numbers_less_or_equal_to_p_is_prime
use warnings;
use ntheory qw( is_prime primes vecsum );
 
print "@{[ grep is_prime( vecsum( @{ primes($_) } ) ), @{ primes(1000) } ]}\n";</syntaxhighlight>
{{out}}
<pre>
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
</pre>
 
=={{header|Phix}}==
As per Raku, this is pretty much an exact duplicate of [[Summarize_primes#Phix]], bar output of primes instead of their index.
<!--<lang Phix>(phixonline)-->
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">sump</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]))</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">),</span><span style="color: #000000;">sump</span><span style="color: #0000FF;">)</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;">"%d found: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
21 found: {2,3,7,13,37,43,281,311,503,541,557,593,619,673,683,733,743,839,881,929,953}
</pre>
=={{header|Prolog}}==
runs with swi-prolog
<syntaxhighlight lang="prolog">
primes(2, Limit):- 2 =< Limit.
primes(3, Limit):- 3 =< Limit.
primes(N, Limit):-
between(5, Limit, N),
N /\ 1 > 0, % odd
N mod 3 > 0, % /= 3*i
M is floor(sqrt(N)) + 1, % reverse 6*I-1
Max is M div 6,
forall(between(1, Max, I), (N mod (6*I-1) > 0, N mod (6*I+1) > 0)).
 
isPrime(N):-
primes(N, inf).
 
primeSum(List, LastP):-
append(SubList, _, List),
sum_list(SubList, Sum),
isPrime(Sum),
last(SubList, LastP).
 
showList(List):-
last(List, Last),
FmtLen is 2 + floor(log10(Last)), % one more for space
swritef(FmtStr, '%%dr', [FmtLen]),
findnsols(10, X, (member(X, List), writef(FmtStr, [X])), _), nl,
fail.
showList(_).
 
do(Limit):-
findall(N, primes(N, Limit), PrimeList),
findall(LastP, primeSum(PrimeList, LastP), SumList),
showList(SumList).
 
do:- do(2000).
</syntaxhighlight>
{{out}}
<pre>
?- do.
2 3 7 13 37 43 281 311 503 541
557 593 619 673 683 733 743 839 881 929
953 1061 1163 1213 1249 1277 1283 1307 1321 1949
true.
</pre>
 
=={{header|Quackery}}==
 
<code>isprime</code> is defined at [[Primality by trial division#Quackery]].
 
<syntaxhighlight lang="Quackery"> 0 1000 times [ i^ isprime if [ i^ + dup isprime if [ i^ echo sp ] drop ] ]</syntaxhighlight>
 
{{out}}
 
<pre>2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953</pre>
 
=={{header|Raku}}==
Trivial variation of [[Summarize_primes#Raku|Summarize primes]] task. Modified to do double duty.
<syntaxhighlight lang="raku" line>use Lingua::EN::Numbers;
 
my @primes = grep *.is-prime, ^Inf;
my @primesums = [\+] @primes;
say "{.elems} cumulative prime sums:\n",
.map( -> $p {
sprintf "The sum of the first %3d (up to {@primes[$p]}) is prime: %s",
1 + $p, comma @primesums[$p]
}
).join("\n")
given grep { @primesums[$_].is-prime }, ^1000;</syntaxhighlight>
{{out}}
<pre>76 cumulative prime sums:
The sum of the first 1 (up to 2) is prime: 2
The sum of the first 2 (up to 3) is prime: 5
The sum of the first 4 (up to 7) is prime: 17
The sum of the first 6 (up to 13) is prime: 41
The sum of the first 12 (up to 37) is prime: 197
The sum of the first 14 (up to 43) is prime: 281
The sum of the first 60 (up to 281) is prime: 7,699
The sum of the first 64 (up to 311) is prime: 8,893
The sum of the first 96 (up to 503) is prime: 22,039
The sum of the first 100 (up to 541) is prime: 24,133
The sum of the first 102 (up to 557) is prime: 25,237
The sum of the first 108 (up to 593) is prime: 28,697
The sum of the first 114 (up to 619) is prime: 32,353
The sum of the first 122 (up to 673) is prime: 37,561
The sum of the first 124 (up to 683) is prime: 38,921
The sum of the first 130 (up to 733) is prime: 43,201
The sum of the first 132 (up to 743) is prime: 44,683
The sum of the first 146 (up to 839) is prime: 55,837
The sum of the first 152 (up to 881) is prime: 61,027
The sum of the first 158 (up to 929) is prime: 66,463
The sum of the first 162 (up to 953) is prime: 70,241
The sum of the first 178 (up to 1061) is prime: 86,453
The sum of the first 192 (up to 1163) is prime: 102,001
The sum of the first 198 (up to 1213) is prime: 109,147
The sum of the first 204 (up to 1249) is prime: 116,533
The sum of the first 206 (up to 1277) is prime: 119,069
The sum of the first 208 (up to 1283) is prime: 121,631
The sum of the first 214 (up to 1307) is prime: 129,419
The sum of the first 216 (up to 1321) is prime: 132,059
The sum of the first 296 (up to 1949) is prime: 263,171
The sum of the first 308 (up to 2029) is prime: 287,137
The sum of the first 326 (up to 2161) is prime: 325,019
The sum of the first 328 (up to 2203) is prime: 329,401
The sum of the first 330 (up to 2213) is prime: 333,821
The sum of the first 332 (up to 2237) is prime: 338,279
The sum of the first 334 (up to 2243) is prime: 342,761
The sum of the first 342 (up to 2297) is prime: 360,979
The sum of the first 350 (up to 2357) is prime: 379,667
The sum of the first 356 (up to 2393) is prime: 393,961
The sum of the first 358 (up to 2411) is prime: 398,771
The sum of the first 426 (up to 2957) is prime: 581,921
The sum of the first 446 (up to 3137) is prime: 642,869
The sum of the first 458 (up to 3251) is prime: 681,257
The sum of the first 460 (up to 3257) is prime: 687,767
The sum of the first 464 (up to 3301) is prime: 700,897
The sum of the first 480 (up to 3413) is prime: 754,573
The sum of the first 484 (up to 3461) is prime: 768,373
The sum of the first 488 (up to 3491) is prime: 782,263
The sum of the first 512 (up to 3671) is prime: 868,151
The sum of the first 530 (up to 3821) is prime: 935,507
The sum of the first 536 (up to 3863) is prime: 958,577
The sum of the first 548 (up to 3947) is prime: 1,005,551
The sum of the first 568 (up to 4129) is prime: 1,086,557
The sum of the first 620 (up to 4583) is prime: 1,313,041
The sum of the first 630 (up to 4657) is prime: 1,359,329
The sum of the first 676 (up to 5051) is prime: 1,583,293
The sum of the first 680 (up to 5087) is prime: 1,603,597
The sum of the first 696 (up to 5233) is prime: 1,686,239
The sum of the first 708 (up to 5351) is prime: 1,749,833
The sum of the first 734 (up to 5563) is prime: 1,891,889
The sum of the first 762 (up to 5807) is prime: 2,051,167
The sum of the first 768 (up to 5849) is prime: 2,086,159
The sum of the first 776 (up to 5897) is prime: 2,133,121
The sum of the first 780 (up to 5939) is prime: 2,156,813
The sum of the first 784 (up to 6007) is prime: 2,180,741
The sum of the first 808 (up to 6211) is prime: 2,327,399
The sum of the first 814 (up to 6263) is prime: 2,364,833
The sum of the first 820 (up to 6301) is prime: 2,402,537
The sum of the first 836 (up to 6427) is prime: 2,504,323
The sum of the first 844 (up to 6529) is prime: 2,556,187
The sum of the first 848 (up to 6563) is prime: 2,582,401
The sum of the first 852 (up to 6581) is prime: 2,608,699
The sum of the first 926 (up to 7243) is prime: 3,120,833
The sum of the first 942 (up to 7433) is prime: 3,238,237
The sum of the first 984 (up to 7757) is prime: 3,557,303
The sum of the first 992 (up to 7853) is prime: 3,619,807</pre>
 
=={{header|REXX}}==
<syntaxhighlight lang="rexx">/*REXX program finds primes in which sum of primes ≤ P is prime, where P < 1.000.*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 1000 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*the width of a number in any column. */
title= ' primes which the sum of primes ≤ P is prime, where P < ' commas(hi)
say ' index │' center(title, 1 + cols*(w+1) )
say '───────┼'center("" , 1 + cols*(w+1), '─')
found= 0; idx = 1 /*number of primes found (so far); IDX.*/
$=; pSum= 0 /*#: list of primes (so far); init pSum*/
do j=1 for hi-1; p= @.j; pSum= pSum+p /*find summation primes within range. */
if \!.pSum then iterate /*Is sum─of─primes a prime? Then skip.*/
found= found + 1 /*bump the number of found primes. */
if cols<0 then iterate /*Build the list (to be shown later)? */
c= commas(p) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a found prime──►list, allow big #*/
if found//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
 
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found ' commas(found) title
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: !.= 0; sP= 0 /*prime semaphores; sP= sum of primes.*/
@.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; sq.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 until @.#>=hi & @.#>sP /*find odd primes where P≥hi and P>sP.*/
parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
do k=5 while sq.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; sq.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
if @.#<hi then sP= sP + @.# /*maybe add this prime to sum─of─primes*/
end /*j*/; return</syntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
index │ primes which the sum of primes ≤ P is prime, where P < 1,000
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 │ 2 3 7 13 37 43 281 311 503 541
11 │ 557 593 619 673 683 733 743 839 881 929
21 │ 953
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────
 
Found 21 primes which the sum of primes ≤ P is prime, where P < 1,000
</pre>
 
=={{header|Ring}}==
<langsyntaxhighlight lang="ring">
load "stdlib.ring"
see "working..." + nl
Line 31 ⟶ 707:
if isprime(sum)
see "" + n + " "
row = row + 1+
if row%5 = 0
see nl
Line 41 ⟶ 717:
see nl + "Found " + row + " numbers" + nl
see "done..." + nl
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 53 ⟶ 729:
Found 21 numbers
done...
</pre>
 
=={{header|RPL}}==
{{works with|HP|49}}
« { } 0 0
'''WHILE''' DUP 1000 < '''REPEAT'''
NEXTPRIME SWAP OVER + SWAP
'''IF''' OVER ISPRIME? '''THEN''' ROT OVER + UNROT '''END'''
'''END''' DROP2
» '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: { 2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953 }
</pre>
 
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func primes_with_prime_sum(n, callback) {
var s = 0
n.each_prime {|p|
s += p
callback(p, s) if s.is_prime
}
}
 
primes_with_prime_sum(1000, {|p,s|
say "prime: #{'%3s' % p} prime sum: #{'%5s' % s}"
})</syntaxhighlight>
{{out}}
<pre>
prime: 2 prime sum: 2
prime: 3 prime sum: 5
prime: 7 prime sum: 17
prime: 13 prime sum: 41
prime: 37 prime sum: 197
prime: 43 prime sum: 281
prime: 281 prime sum: 7699
prime: 311 prime sum: 8893
prime: 503 prime sum: 22039
prime: 541 prime sum: 24133
prime: 557 prime sum: 25237
prime: 593 prime sum: 28697
prime: 619 prime sum: 32353
prime: 673 prime sum: 37561
prime: 683 prime sum: 38921
prime: 733 prime sum: 43201
prime: 743 prime sum: 44683
prime: 839 prime sum: 55837
prime: 881 prime sum: 61027
prime: 929 prime sum: 66463
prime: 953 prime sum: 70241
</pre>
 
=={{header|Uiua}}==
{{works with|Uiua|0.10.0-dev.1}}
<syntaxhighlight lang="Uiua">
# Build primes by sieve. Limit found by inspection.
⇌◌⍢(▽≠0◿⊃⊢(.↘1)⟜(⊂⊢)|>0⧻) ↘2⇡80000 []
# Build running sums.
\+▽<1000...
# # Find sums that are prime, then prettify.
⧻.⍉⊟:∩(⬚0▽),⟜∊
 
</syntaxhighlight>
{{out}}
<pre>
╭─
╷ 2 2
3 5
7 17
13 41
37 197
43 281
281 7699
311 8893
503 22039
541 24133
557 25237
593 28697
619 32353
673 37561
683 38921
733 43201
743 44683
839 55837
881 61027
929 66463
953 70241
╯
21
</pre>
 
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./math" for Int, Nums
import "./fmt" for Fmt
 
var primes = Int.primeSieve(1000, true)
var maxSum = Nums.sum(primes)
var c = Int.primeSieve(maxSum, false)
var primeSum = 0
var results = []
for (p in primes) {
primeSum = primeSum + p
if (!c[primeSum]) results.add(p)
}
System.print("Primes 'p' under 1000 where the sum of all primes <= p is also prime:")
Fmt.tprint("$4d", results, 7)
System.print("\nFound %(results.count) such primes.")</syntaxhighlight>
 
{{out}}
<pre>
Primes 'p' under 1000 where the sum of all primes <= p is also prime:
2 3 7 13 37 43 281
311 503 541 557 593 619 673
683 733 743 839 881 929 953
 
Found 21 such primes.
</pre>
 
=={{header|XPL0}}==
<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, N, Sum;
[Count:= 0;
Sum:= 0;
for N:= 2 to 1000-1 do
if IsPrime(N) then
[Sum:= Sum + N;
if IsPrime(Sum) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
];
];
CrLf(0);
IntOut(0, Count);
Text(0, " such numbers found below 1000.
");
]</syntaxhighlight>
{{out}}
<pre>2 3 7 13 37 43 281 311 503 541
557 593 619 673 683 733 743 839 881 929
953
21 such numbers found below 1000.
</pre>
Midaz
60

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