Prime numbers p for which the sum of primes less than or equal to p is prime
Prime numbers p for which the sum of primes less than or equal to p is prime 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.
- Task
Find primes p for which the sum of primes less than or equal to p is prime, where p < 1,000.
ALGOL 68
Same as the Summarize primes#ALGOL_68 solution.
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- Output:
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
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
- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
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)
}
- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953 1-999: 21
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;
- Output:
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.
EasyLang
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
fastfunc nextprim prim .
repeat
prim += 1
until isprim prim = 1
.
return prim
.
prim = 2
repeat
sum += prim
if isprim sum = 1
write prim & " "
.
prim = nextprim prim
until prim >= 1000
.
- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
F#
This task uses Extensible Prime Generator (F#)
// 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 ""
Factor
USING: assocs assocs.extras kernel math.primes math.statistics
prettyprint ;
1000 primes-upto dup cum-sum zip [ prime? ] filter-values .
- Output:
{
{ 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 }
}
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
- Output:
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.
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")
}
- Output:
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
J
(#~ 1 p: +/\)@(i.&.(p:^:_1)) 1000
- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
jq
Works with gojq, the Go implementation of jq
This entry adopts the straightforward approach as used for example in the 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 entry.
See Erdős-primes#jq for a suitable definition of `is_prime` as used here.
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)- Output:
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.
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))
- Output:
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
Mathematica / Wolfram Language
cands = Most@NestWhileList[NextPrime, 2, # < 1000 &];
Partition[
cands[[Flatten@Position[PrimeQ /@ Accumulate[cands], True]]],
UpTo[5]] // TableForm
- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
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
- Output:
21 found: [2, 3, 7, 13, 37, 43, 281, 311, 503, 541, 557, 593, 619, 673, 683, 733, 743, 839, 881, 929, 953
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(" ")
- Output:
Found 21 primes: 2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
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";
- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
Phix
As per Raku, this is pretty much an exact duplicate of Summarize_primes#Phix, bar output of primes instead of their index.
function sump(integer p, i, sequence s) return is_prime(sum(s[1..i])) end function sequence res = filter(get_primes_le(1000),sump) printf(1,"%d found: %V\n",{length(res),res})
- Output:
21 found: {2,3,7,13,37,43,281,311,503,541,557,593,619,673,683,733,743,839,881,929,953}
Prolog
runs with swi-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).
- Output:
?- 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.
Python
def prime(n):
for i in range(2, int(n ** 0.5) + 1):
if n % i == 0:
return False
return True
p = []
x = 1
lis = []
for i in range(0, 1000):
x += 1
if prime(x) == True:
p.append(x)
str_x = str(x)
if prime(sum(p)) == True:
lis.append(x)
if int(x) == 1000:
print(f'Found {len(lis)} primes less than 1000')
for i in lis:
print(i)
- Output:
Found 21 primes less than 1000 2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
Quackery
isprime is defined at Primality by trial division#Quackery.
0 1000 times [ i^ isprime if [ i^ + dup isprime if [ i^ echo sp ] drop ] ]- Output:
2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953
Raku
Trivial variation of Summarize primes task. Modified to do double duty.
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;
- Output:
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
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
- output when using the default inputs:
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
Ring
load "stdlib.ring"
see "working..." + nl
see "Prime numbers p which sum of prime numbers less or equal to p is prime:" + nl
row = 0
sum = 0
limit = 1000
for n = 1 to limit
if isprime(n)
sum = sum + n
if isprime(sum)
see "" + n + " "
row++
if row%5 = 0
see nl
ok
ok
ok
next
see nl + "Found " + row + " numbers" + nl
see "done..." + nl- Output:
working... Prime numbers p which sum of prime numbers less or equal to p is prime: 2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953 Found 21 numbers done...
RPL
« { } 0 0
WHILE DUP 1000 < REPEAT
NEXTPRIME SWAP OVER + SWAP
IF OVER ISPRIME? THEN ROT OVER + UNROT END
END DROP2
» 'TASK' STO
- Output:
1: { 2 3 7 13 37 43 281 311 503 541 557 593 619 673 683 733 743 839 881 929 953 }
Sidef
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}"
})
- Output:
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
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▽),⟜∊- Output:
╭─
╷ 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
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.")
- Output:
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.
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.
");
]- Output:
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.