Prime numbers p for which the sum of primes less than or equal to p is prime
Find primes p which the sum of primes less or equal to p is prime, where p < 1,000.
- Task
Factor
<lang factor>USING: assocs assocs.extras kernel math.primes math.statistics prettyprint ;
1000 primes-upto dup cum-sum zip [ prime? ] filter-values .</lang>
- 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 }
}
Go
<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")
}</lang>
- 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
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}
Raku
Trivial variation of Summarize primes task. Modified to do double duty. <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 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</lang>
- 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
<lang 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 = row + 1
if row%5 = 0
see nl
ok
ok
ok
next
see nl + "Found " + row + " numbers" + nl see "done..." + nl </lang>
- 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...
Wren
<lang ecmascript>import "/math" for Int, Nums import "/seq" for Lst 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:") for (chunk in Lst.chunks(results, 7)) Fmt.print("$4d", chunk) System.print("\nFound %(results.count) such primes.")</lang>
- 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
<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, M, Sum; [Count:= 0; for N:= 2 to 1000-1 do
if IsPrime(N) then
[Sum:= 0;
for M:= 2 to N do
if IsPrime(M) then
Sum:= Sum + M;
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. "); ]</lang>
- 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.