Summarize primes
Summarize primes 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
Considering in order of length, n, all sequences of consecutive
primes, p, from 2 onwards, where p < 1000 and n>0, select those
sequences whose sum is prime, and for these display the length of the
sequence, the last item in the sequence, and the sum.
ALGOL 68
<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 </lang>
- 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
ALGOL W
<lang algolw>begin % sum the primes below n and report the sums that are prime %
integer MAX_NUMBER;
MAX_NUMBER := 999;
begin
logical array prime( 1 :: MAX_NUMBER );
integer primeCount, primeSum, primeSumCount;
% sieve the primes to MAX_NUMBER %
prime( 1 ) := false; prime( 2 ) := true;
for i := 3 step 2 until MAX_NUMBER do prime( i ) := true;
for i := 4 step 2 until MAX_NUMBER do prime( i ) := false;
for i := 3 step 2 until truncate( sqrt( MAX_NUMBER ) ) do begin
integer ii; ii := i + i;
if prime( i ) then begin
for p := i * i step ii until MAX_NUMBER do prime( p ) := false
end if_prime_i
end for_i ;
% find the prime sums that are prime %
primeCount := primeSum := primeSumCount := 0;
write( "prime prime" );
write( "count sum" );
for i := 1 until MAX_NUMBER do begin
if prime( i ) then begin
% have another prime %
logical isPrime;
primeSum := primeSum + i;
primeCount := primeCount + 1;
% check whether the prime sum is also prime %
isPrime := true;
for p := 1 until i div 2 do begin
if prime( p ) then begin
isPrime := primeSum rem p not = 0;
if not isPrime then goto endPrimeCheck
end if_prime_p
end for_p ;
endPrimeCheck:
if isPrime then begin
% the prime sum is also prime %
primeSumCount := primeSumCount + 1;
write( i_w := 5, s_w := 0
, primeCount
, " "
, i_w := 6
, primeSum
)
end if_isPrime
end if_prime_i
end for_i ;
write();
write( i_w := 1, s_w := 0
, "Found "
, primeSumCount
, " prime sums of primes below "
, MAX_NUMBER + 1
)
end
end.</lang>
- Output:
prime prime
count sum
1 2
2 5
4 17
6 41
12 197
14 281
60 7699
64 8893
96 22039
100 24133
102 25237
108 28697
114 32353
122 37561
124 38921
130 43201
132 44683
146 55837
152 61027
158 66463
162 70241
Found 21 prime sums of primes below 1000
Arturo
<lang rebol>print (pad "index" 6) ++ " | " ++
(pad "prime" 6) ++ " | " ++
(pad "prime sum" 11)
print "------------------------------"
s: 0 idx: 0 loop 2..999 'n [
if prime? n [
idx: idx + 1
s: s + n
if prime? s ->
print (pad to :string idx 6) ++ " | " ++
(pad to :string n 6) ++ " | " ++
(pad to :string s 11)
]
]</lang>
- Output:
index | prime | 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
AWK
<lang AWK>
- syntax: GAWK -f SUMMARIZE_PRIMES.AWK
BEGIN {
start = 1
stop = 999
for (i=start; i<=stop; i++) {
if (is_prime(i)) {
count1++
sum += i
if (is_prime(sum)) {
printf("the sum of %3d primes from primes 2-%-3s is %5d which is also prime\n",count1,i,sum)
count2++
}
}
}
printf("Summarized primes %d-%d: %d\n",start,stop,count2)
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)
} </lang>
- Output:
the sum of 1 primes from primes 2-2 is 2 which is also prime the sum of 2 primes from primes 2-3 is 5 which is also prime the sum of 4 primes from primes 2-7 is 17 which is also prime the sum of 6 primes from primes 2-13 is 41 which is also prime the sum of 12 primes from primes 2-37 is 197 which is also prime the sum of 14 primes from primes 2-43 is 281 which is also prime the sum of 60 primes from primes 2-281 is 7699 which is also prime the sum of 64 primes from primes 2-311 is 8893 which is also prime the sum of 96 primes from primes 2-503 is 22039 which is also prime the sum of 100 primes from primes 2-541 is 24133 which is also prime the sum of 102 primes from primes 2-557 is 25237 which is also prime the sum of 108 primes from primes 2-593 is 28697 which is also prime the sum of 114 primes from primes 2-619 is 32353 which is also prime the sum of 122 primes from primes 2-673 is 37561 which is also prime the sum of 124 primes from primes 2-683 is 38921 which is also prime the sum of 130 primes from primes 2-733 is 43201 which is also prime the sum of 132 primes from primes 2-743 is 44683 which is also prime the sum of 146 primes from primes 2-839 is 55837 which is also prime the sum of 152 primes from primes 2-881 is 61027 which is also prime the sum of 158 primes from primes 2-929 is 66463 which is also prime the sum of 162 primes from primes 2-953 is 70241 which is also prime Summarized primes 1-999: 21
C
<lang c>#include <stdbool.h>
- include <stdio.h>
bool is_prime(int n) {
int i = 5;
if (n < 2) {
return false;
}
if (n % 2 == 0) {
return n == 2;
}
if (n % 3 == 0) {
return n == 3;
}
while (i * i <= n) {
if (n % i == 0) {
return false;
}
i += 2;
if (n % i == 0) {
return false;
}
i += 4;
}
return true;
}
int main() {
const int start = 1; const int stop = 1000;
int sum = 0; int count = 0; int sc = 0; int p;
for (p = start; p < stop; p++) {
if (is_prime(p)) {
count++;
sum += p;
if (is_prime(sum)) {
printf("The sum of %3d primes in [2, %3d] is %5d which is also prime\n", count, p, sum);
sc++;
}
}
}
printf("There are %d summerized primes in [%d, %d)\n", sc, start, stop);
return 0;
}</lang>
- Output:
The sum of 1 primes in [2, 2] is 2 which is also prime The sum of 2 primes in [2, 3] is 5 which is also prime The sum of 4 primes in [2, 7] is 17 which is also prime The sum of 6 primes in [2, 13] is 41 which is also prime The sum of 12 primes in [2, 37] is 197 which is also prime The sum of 14 primes in [2, 43] is 281 which is also prime The sum of 60 primes in [2, 281] is 7699 which is also prime The sum of 64 primes in [2, 311] is 8893 which is also prime The sum of 96 primes in [2, 503] is 22039 which is also prime The sum of 100 primes in [2, 541] is 24133 which is also prime The sum of 102 primes in [2, 557] is 25237 which is also prime The sum of 108 primes in [2, 593] is 28697 which is also prime The sum of 114 primes in [2, 619] is 32353 which is also prime The sum of 122 primes in [2, 673] is 37561 which is also prime The sum of 124 primes in [2, 683] is 38921 which is also prime The sum of 130 primes in [2, 733] is 43201 which is also prime The sum of 132 primes in [2, 743] is 44683 which is also prime The sum of 146 primes in [2, 839] is 55837 which is also prime The sum of 152 primes in [2, 881] is 61027 which is also prime The sum of 158 primes in [2, 929] is 66463 which is also prime The sum of 162 primes in [2, 953] is 70241 which is also prime There are 21 summerized primes in [1, 1000)
C++
<lang cpp>#include <iostream>
bool is_prime(int n) {
if (n < 2) {
return false;
}
if (n % 2 == 0) {
return n == 2;
}
if (n % 3 == 0) {
return n == 3;
}
int i = 5;
while (i * i <= n) {
if (n % i == 0) {
return false;
}
i += 2;
if (n % i == 0) {
return false;
}
i += 4;
}
return true;
}
int main() {
const int start = 1; const int stop = 1000;
int sum = 0; int count = 0; int sc = 0;
for (int p = start; p < stop; p++) {
if (is_prime(p)) {
count++;
sum += p;
if (is_prime(sum)) {
printf("The sum of %3d primes in [2, %3d] is %5d which is also prime\n", count, p, sum);
sc++;
}
}
}
printf("There are %d summerized primes in [%d, %d)\n", sc, start, stop);
return 0;
}</lang>
- Output:
The sum of 1 primes in [2, 2] is 2 which is also prime The sum of 2 primes in [2, 3] is 5 which is also prime The sum of 4 primes in [2, 7] is 17 which is also prime The sum of 6 primes in [2, 13] is 41 which is also prime The sum of 12 primes in [2, 37] is 197 which is also prime The sum of 14 primes in [2, 43] is 281 which is also prime The sum of 60 primes in [2, 281] is 7699 which is also prime The sum of 64 primes in [2, 311] is 8893 which is also prime The sum of 96 primes in [2, 503] is 22039 which is also prime The sum of 100 primes in [2, 541] is 24133 which is also prime The sum of 102 primes in [2, 557] is 25237 which is also prime The sum of 108 primes in [2, 593] is 28697 which is also prime The sum of 114 primes in [2, 619] is 32353 which is also prime The sum of 122 primes in [2, 673] is 37561 which is also prime The sum of 124 primes in [2, 683] is 38921 which is also prime The sum of 130 primes in [2, 733] is 43201 which is also prime The sum of 132 primes in [2, 743] is 44683 which is also prime The sum of 146 primes in [2, 839] is 55837 which is also prime The sum of 152 primes in [2, 881] is 61027 which is also prime The sum of 158 primes in [2, 929] is 66463 which is also prime The sum of 162 primes in [2, 953] is 70241 which is also prime There are 21 summerized primes in [1, 1000)
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // Summarize Primes: Nigel Galloway. April 16th., 2021 primes32()|>Seq.takeWhile((>)1000)|>Seq.scan(fun(n,g) p->(n+1,g+p))(0,0)|>Seq.filter(snd>>isPrime)|>Seq.iter(fun(n,g)->printfn "%3d->%d" n g) </lang>
- Output:
1->2 2->5 4->17 6->41 12->197 14->281 60->7699 64->8893 96->22039 100->24133 102->25237 108->28697 114->32353 122->37561 124->38921 130->43201 132->44683 146->55837 152->61027 158->66463 162->70241 Real: 00:00:00.015
Factor
<lang factor>USING: assocs formatting kernel math.primes math.ranges math.statistics prettyprint ;
1000 [ [1,b] ] [ primes-upto cum-sum ] bi zip [ nip prime? ] assoc-filter [ "The sum of the first %3d primes is %5d (which is prime).\n" printf ] assoc-each</lang>
- Output:
The sum of the first 1 primes is 2 (which is prime). The sum of the first 2 primes is 5 (which is prime). The sum of the first 4 primes is 17 (which is prime). The sum of the first 6 primes is 41 (which is prime). The sum of the first 12 primes is 197 (which is prime). The sum of the first 14 primes is 281 (which is prime). The sum of the first 60 primes is 7699 (which is prime). The sum of the first 64 primes is 8893 (which is prime). The sum of the first 96 primes is 22039 (which is prime). The sum of the first 100 primes is 24133 (which is prime). The sum of the first 102 primes is 25237 (which is prime). The sum of the first 108 primes is 28697 (which is prime). The sum of the first 114 primes is 32353 (which is prime). The sum of the first 122 primes is 37561 (which is prime). The sum of the first 124 primes is 38921 (which is prime). The sum of the first 130 primes is 43201 (which is prime). The sum of the first 132 primes is 44683 (which is prime). The sum of the first 146 primes is 55837 (which is prime). The sum of the first 152 primes is 61027 (which is prime). The sum of the first 158 primes is 66463 (which is prime). The sum of the first 162 primes is 70241 (which is prime).
Fermat
<lang fermat>n:=0 s:=0 for i=1, 162 do s:=s+Prime(i);if Isprime(s)=1 then n:=n+1;!!(n,Prime(i),s) fi od </lang>
- Output:
1 2 2 2 3 5 3 7 17 4 13 41 5 37 197 6 43 281 7 281 7699 8 311 8893 9 503 22039 10 541 24133 11 557 25237 12 593 28697 13 619 32353 14 673 37561 15 683 38921 16 733 43201 17 743 44683 18 839 55837 19 881 61027 20 929 66463 21 953 70241
Forth
<lang forth>: prime? ( n -- flag )
dup 2 < if drop false exit then dup 2 mod 0= if 2 = exit then dup 3 mod 0= if 3 = exit then 5 begin 2dup dup * >= while 2dup mod 0= if 2drop false exit then 2 + 2dup mod 0= if 2drop false exit then 4 + repeat 2drop true ;
- main
0 0 { count sum }
." count prime sum" cr
1000 2 do
i prime? if
count 1+ to count
sum i + to sum
sum prime? if
." " count 3 .r ." " i 3 .r ." " sum 5 .r cr
then
then
loop ;
main bye</lang>
- Output:
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
FreeBASIC
<lang freebasic>#include "isprime.bas"
print 1,2,2 dim as integer sum = 2, i, n=1 for i = 3 to 999 step 2
if isprime(i) then
sum += i
n+=1
if isprime(sum) then
print n, i, sum
end if
end if
next i</lang>
- Output:
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
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
Go
<lang go>package main
import (
"fmt" "rcu"
)
func main() {
primes := rcu.Primes(999)
sum, n, c := 0, 0, 0
fmt.Println("Summing the first n primes (<1,000) where the sum is itself prime:")
fmt.Println(" n cumulative sum")
for _, p := range primes {
n++
sum += p
if rcu.IsPrime(sum) {
c++
fmt.Printf("%3d %6s\n", n, rcu.Commatize(sum))
}
}
fmt.Println()
fmt.Println(c, "such prime sums found")
}</lang>
- Output:
Same as Wren example.
Haskell
<lang haskell>import Data.List (scanl) import Data.Numbers.Primes (isPrime, primes)
PRIME SUMS OF FIRST N PRIMES -------------
indexedPrimeSums :: [(Integer, Integer, Integer)] indexedPrimeSums =
filter (\(_, _, n) -> isPrime n) $
scanl
(\(i, _, m) p -> (succ i, p, p + m))
(0, 0, 0)
primes
TEST -------------------------
main :: IO () main =
mapM_ print $ takeWhile (\(_, p, _) -> 1000 > p) indexedPrimeSums
</lang>
- Output:
(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)
jq
Works with gojq, the Go implementation of jq <lang jq>def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else {i:23}
| until( (.i * .i) > $n or ($n % .i == 0); .i += 2)
| .i * .i > $n
end;
- primes up to but excluding $n
def primes($n): [range(2;$n) | select(is_prime)];
"Prime sums of primes less than 1000", (primes(1000)
| . as $p1000 | range(1; length) | ($p1000[: .] | add) as $sum | select($sum | is_prime) | "The sum of the \(.) primes from 2 to \($p1000[.-1]) is \($sum)." )
</lang>
- Output:
Prime sums of primes less than 1000 The sum of the 1 primes from 2 to 2 is 2. The sum of the 2 primes from 2 to 3 is 5. The sum of the 4 primes from 2 to 7 is 17. The sum of the 6 primes from 2 to 13 is 41. The sum of the 12 primes from 2 to 37 is 197. The sum of the 14 primes from 2 to 43 is 281. The sum of the 60 primes from 2 to 281 is 7699. The sum of the 64 primes from 2 to 311 is 8893. The sum of the 96 primes from 2 to 503 is 22039. The sum of the 100 primes from 2 to 541 is 24133. The sum of the 102 primes from 2 to 557 is 25237. The sum of the 108 primes from 2 to 593 is 28697. The sum of the 114 primes from 2 to 619 is 32353. The sum of the 122 primes from 2 to 673 is 37561. The sum of the 124 primes from 2 to 683 is 38921. The sum of the 130 primes from 2 to 733 is 43201. The sum of the 132 primes from 2 to 743 is 44683. The sum of the 146 primes from 2 to 839 is 55837. The sum of the 152 primes from 2 to 881 is 61027. The sum of the 158 primes from 2 to 929 is 66463. The sum of the 162 primes from 2 to 953 is 70241.
Julia
<lang julia>using Primes
p1000 = primes(1000)
for n in 1:length(p1000)
parray = p1000[1:n]
sparray = sum(parray)
if isprime(sparray)
println("The sum of the $n primes from prime 2 to prime $(p1000[n]) is $sparray, which is prime.")
end
end
</lang>
- Output:
The sum of the 1 primes from prime 2 to prime 2 is 2, which is prime. The sum of the 2 primes from prime 2 to prime 3 is 5, which is prime. The sum of the 4 primes from prime 2 to prime 7 is 17, which is prime. The sum of the 6 primes from prime 2 to prime 13 is 41, which is prime. The sum of the 12 primes from prime 2 to prime 37 is 197, which is prime. The sum of the 14 primes from prime 2 to prime 43 is 281, which is prime. The sum of the 60 primes from prime 2 to prime 281 is 7699, which is prime. The sum of the 64 primes from prime 2 to prime 311 is 8893, which is prime. The sum of the 96 primes from prime 2 to prime 503 is 22039, which is prime. The sum of the 100 primes from prime 2 to prime 541 is 24133, which is prime. The sum of the 102 primes from prime 2 to prime 557 is 25237, which is prime. The sum of the 108 primes from prime 2 to prime 593 is 28697, which is prime. The sum of the 114 primes from prime 2 to prime 619 is 32353, which is prime. The sum of the 122 primes from prime 2 to prime 673 is 37561, which is prime. The sum of the 124 primes from prime 2 to prime 683 is 38921, which is prime. The sum of the 130 primes from prime 2 to prime 733 is 43201, which is prime. The sum of the 132 primes from prime 2 to prime 743 is 44683, which is prime. The sum of the 146 primes from prime 2 to prime 839 is 55837, which is prime. The sum of the 152 primes from prime 2 to prime 881 is 61027, which is prime. The sum of the 158 primes from prime 2 to prime 929 is 66463, which is prime. The sum of the 162 primes from prime 2 to prime 953 is 70241, which is prime.
Nim
<lang Nim>import math, strformat
const N = 999
func isPrime(n: Positive): bool =
if (n and 1) == 0: return n == 2 if (n mod 3) == 0: return n == 3 var d = 5 var delta = 2 while d <= sqrt(n.toFloat).int: if n mod d == 0: return false inc d, delta delta = 6 - delta result = true
echo "index prime prime sum" var s = 0 var idx = 0 for n in 2..N:
if n.isPrime:
inc idx
s += n
if s.isPrime: echo &"{idx:3} {n:5} {s:7}"</lang>
- Output:
index prime 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
Perl
<lang perl>use strict; use warnings; use ntheory <nth_prime is_prime>;
my($n, $s, $limit, @sums) = (0, 0, 1000); do {
push @sums, sprintf '%3d %8d', $n, $s if is_prime($s += nth_prime ++$n)
} until $n >= $limit;
print "Of the first $limit primes: @{[scalar @sums]} cumulative prime sums:\n", join "\n", @sums;</lang>
- Output:
Of the first 1000 primes: 76 cumulative prime sums: 1 2 2 5 4 17 6 41 12 197 14 281 60 7699 64 8893 96 22039 100 24133 102 25237 108 28697 114 32353 122 37561 124 38921 130 43201 132 44683 146 55837 152 61027 158 66463 162 70241 178 86453 192 102001 198 109147 204 116533 206 119069 208 121631 214 129419 216 132059 296 263171 308 287137 326 325019 328 329401 330 333821 332 338279 334 342761 342 360979 350 379667 350 379667 356 393961 358 398771 426 581921 446 642869 458 681257 460 687767 464 700897 480 754573 484 768373 488 782263 512 868151 530 935507 536 958577 548 1005551 568 1086557 620 1313041 630 1359329 676 1583293 680 1603597 696 1686239 708 1749833 734 1891889 762 2051167 768 2086159 776 2133121 780 2156813 784 2180741 808 2327399 814 2364833 820 2402537 836 2504323 844 2556187 848 2582401 852 2608699 926 3120833 942 3238237 984 3557303 992 3619807
Phix
function sp(integer n) return is_prime(sum(get_primes(-n))) end function sequence res = apply(filter(tagset(length(get_primes_le(1000))),sp),sprint) printf(1,"Found %d of em: %s\n",{length(res),join(shorten(res,"",5),", ")})
- Output:
Found 21 of em: 1, 2, 4, 6, 12, ..., 132, 146, 152, 158, 162
Python
<lang python>Prime sums of primes up to 1000
from itertools import accumulate, chain, takewhile
- primeSums :: [(Int, (Int, Int))]
def primeSums():
Non finite stream of enumerated tuples,
in which the first value is a prime,
and the second the sum of that prime and all
preceding primes.
return (
x for x in enumerate(
accumulate(
chain([(0, 0)], primes()),
lambda a, p: (p, p + a[1])
)
) if isPrime(x[1][1])
)
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
Prime sums of primes below 1000
for x in takewhile(
lambda t: 1000 > t[1][0],
primeSums()
):
print(f'{x[0]} -> {x[1][1]}')
- ----------------------- GENERIC ------------------------
- isPrime :: Int -> Bool
def isPrime(n):
True if n is prime.
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False
def p(x):
return 0 == n % x or 0 == n % (2 + x)
return not any(map(p, range(5, 1 + int(n ** 0.5), 6)))
- primes :: [Int]
def primes():
Non finite sequence of prime numbers.
n = 2
dct = {}
while True:
if n in dct:
for p in dct[n]:
dct.setdefault(n + p, []).append(p)
del dct[n]
else:
yield n
dct[n * n] = [n]
n = 1 + n
- MAIN ---
if __name__ == '__main__':
main()
</lang>
- Output:
1 -> 2 2 -> 5 4 -> 17 6 -> 41 12 -> 197 14 -> 281 60 -> 7699 64 -> 8893 96 -> 22039 100 -> 24133 102 -> 25237 108 -> 28697 114 -> 32353 122 -> 37561 124 -> 38921 130 -> 43201 132 -> 44683 146 -> 55837 152 -> 61027 158 -> 66463 162 -> 70241
Raku
<lang perl6>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;</lang>
- 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
<lang rexx>/*REXX pgm finds summation primes P, primes which the sum of primes up to P are prime. */ parse arg hi . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 1000 /*Not specified? Then use the default.*/ call genP /*build array of semaphores for primes.*/ w= 30; w2= w*2%3; pad= left(,w-w2) /*the width of the columns two & three.*/ title= ' summation primes which the sum of primes up to P is also prime, P < ' ,
commas(hi)
say ' index │' center(subword(title, 1, 2), w) center('prime sum', w) /*display title.*/ say '───────┼'center("" , 1 + (w+1)*2, '─') /* " sep. */ found= 0 /*initialize # of summation primes. */
$= 0 /*sum of primes up to the current prime*/
do j=1 for hi-1; p= @.j; $= $ + p /*find summation primes within range. */
if \!.$ then iterate /*Is sum─of─primes a prime? Then skip.*/
found= found + 1 /*bump the number of summation primes. */
say right(j, 6) '│'strip( right(commas(p), w2)pad || right(commas($), w2), "T")
end /*j*/
say '───────┴'center("" , 1 + (w+1)*2, '─') /*display foot separator after output. */ 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 ÷ by 5? (right digit)*/
if j//3==0 then iterate; if j//7==0 then iterate /*J ÷ by 3?; J ÷ by 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 # Ps; assign next P; P square; P*/
if @.#<hi then sP= sP + @.# /*maybe add this prime to sum─of─primes*/
end /*j*/; return</lang>
- output when using the default inputs:
index │ summation primes prime sum
───────┼───────────────────────────────────────────────────────────────
1 │ 2 2
2 │ 3 5
4 │ 7 17
6 │ 13 41
12 │ 37 197
14 │ 43 281
60 │ 281 7,699
64 │ 311 8,893
96 │ 503 22,039
100 │ 541 24,133
102 │ 557 25,237
108 │ 593 28,697
114 │ 619 32,353
122 │ 673 37,561
124 │ 683 38,921
130 │ 733 43,201
132 │ 743 44,683
146 │ 839 55,837
152 │ 881 61,027
158 │ 929 66,463
162 │ 953 70,241
───────┴───────────────────────────────────────────────────────────────
Found 21 summation primes which the sum of primes up to P is also prime, P < 1,000
Ring
<lang ring> load "stdlib.ring" see "working..." + nl see "Summarize primes:" + nl see "n sum" + nl row = 0 sum = 0 limit = 1000 Primes = []
for n = 2 to limit
if isprime(n)
add(Primes,n)
ok
next
for n = 1 to len(Primes)
sum = sum + Primes[n]
if isprime(sum)
row = row + 1
see "" + n + " " + sum + nl
ok
next
see "Found " + row + " numbers" + nl see "done..." + nl </lang>
- Output:
working... Summarize primes: n sum 1 2 2 5 4 17 6 41 12 197 14 281 60 7699 64 8893 96 22039 100 24133 102 25237 108 28697 114 32353 122 37561 124 38921 130 43201 132 44683 146 55837 152 61027 158 66463 162 70241 Found 21 numbers done...
Ruby
<lang ruby>def isPrime(n)
if n < 2 then
return false
end
if n % 2 == 0 then
return n == 2
end
if n % 3 == 0 then
return n == 3
end
i = 5
while i * i <= n
if n % i == 0 then
return false
end
i += 2
if n % i == 0 then
return false
end
i += 4
end
return true
end
START = 1 STOP = 1000
sum = 0 count = 0 sc = 0
for p in START .. STOP
if isPrime(p) then
count += 1
sum += p
if isPrime(sum) then
print "The sum of %3d primes in [2, %3d] is %5d which is also prime\n" % [count, p, sum]
sc += 1
end
end
end print "There are %d summerized primes in [%d, %d]\n" % [sc, START, STOP]</lang>
- Output:
The sum of 1 primes in [2, 2] is 2 which is also prime The sum of 2 primes in [2, 3] is 5 which is also prime The sum of 4 primes in [2, 7] is 17 which is also prime The sum of 6 primes in [2, 13] is 41 which is also prime The sum of 12 primes in [2, 37] is 197 which is also prime The sum of 14 primes in [2, 43] is 281 which is also prime The sum of 60 primes in [2, 281] is 7699 which is also prime The sum of 64 primes in [2, 311] is 8893 which is also prime The sum of 96 primes in [2, 503] is 22039 which is also prime The sum of 100 primes in [2, 541] is 24133 which is also prime The sum of 102 primes in [2, 557] is 25237 which is also prime The sum of 108 primes in [2, 593] is 28697 which is also prime The sum of 114 primes in [2, 619] is 32353 which is also prime The sum of 122 primes in [2, 673] is 37561 which is also prime The sum of 124 primes in [2, 683] is 38921 which is also prime The sum of 130 primes in [2, 733] is 43201 which is also prime The sum of 132 primes in [2, 743] is 44683 which is also prime The sum of 146 primes in [2, 839] is 55837 which is also prime The sum of 152 primes in [2, 881] is 61027 which is also prime The sum of 158 primes in [2, 929] is 66463 which is also prime The sum of 162 primes in [2, 953] is 70241 which is also prime There are 21 summerized primes in [1, 1000]
Rust
<lang rust>// [dependencies] // primal = "0.3"
fn main() {
let limit = 1000;
let mut sum = 0;
println!("count prime sum");
for (n, p) in primal::Sieve::new(limit)
.primes_from(2)
.take_while(|x| *x < limit)
.enumerate()
{
sum += p;
if primal::is_prime(sum as u64) {
println!(" {:>3} {:>3} {:>5}", n + 1, p, sum);
}
}
}</lang>
- Output:
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
Sidef
<lang ruby>1000.primes.map_reduce {|a,b| a + b }.map_kv {|k,v|
[k+1, prime(k+1), v]
}.grep { .tail.is_prime }.prepend(
['count', 'prime', 'sum']
).each_2d {|n,p,s|
printf("%5s %6s %8s\n", n, p, s)
}</lang>
- Output:
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
Wren
<lang ecmascript>import "/math" for Int import "/fmt" for Fmt
var primes = Int.primeSieve(999) var sum = 0 var n = 0 var c = 0 System.print("Summing the first n primes (<1,000) where the sum is itself prime:") System.print(" n cumulative sum") for (p in primes) {
n = n + 1
sum = sum + p
if (Int.isPrime(sum)) {
c = c + 1
Fmt.print("$3d $,6d", n, sum)
}
} System.print("\n%(c) such prime sums found")</lang>
- Output:
Summing the first n primes (<1,000) where the sum is itself prime: n cumulative sum 1 2 2 5 4 17 6 41 12 197 14 281 60 7,699 64 8,893 96 22,039 100 24,133 102 25,237 108 28,697 114 32,353 122 37,561 124 38,921 130 43,201 132 44,683 146 55,837 152 61,027 158 66,463 162 70,241 21 such prime sums found
XPL0
<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, Prime; [Text(0, "Prime Prime count sum "); Count:= 0; N:= 0; Sum:= 0; for Prime:= 2 to 1000-1 do
if IsPrime(Prime) then
[N:= N+1;
Sum:= Sum + Prime;
if IsPrime(Sum) then
[Count:= Count+1;
IntOut(0, N);
ChOut(0, 9\tab\);
IntOut(0, Sum);
CrLf(0);
];
];
IntOut(0, Count); Text(0, " prime sums of primes found below 1000. "); ]</lang>
- Output:
Prime Prime count sum 1 2 2 5 4 17 6 41 12 197 14 281 60 7699 64 8893 96 22039 100 24133 102 25237 108 28697 114 32353 122 37561 124 38921 130 43201 132 44683 146 55837 152 61027 158 66463 162 70241 21 prime sums of primes found below 1000.