Extreme primes

Extreme 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.
Definition

Write down the first prime number, add the next prime number and if it is prime, add it to the series and so on. These primes are called extreme primes.

Stretch

Find and display the 1,000th, 2,000th, 3,000th, 4,000th and 5,000th extreme primes and for each one show the prime number p up to and including which primes need to be summed to obtain it.

Reference

ALGOL 68

```BEGIN # sum the primes below n and report the sums that are prime            #
PR read "primes.incl.a68" PR                   # include prime utilities #
[]BOOL prime = PRIMESIEVE 2 000 000;     # sieve the primes to 2 000 000 #
# returns TRUE if n is prime, FALSE otherwise                            #
PROC is prime = ( LONG INT n )BOOL:
IF   n <= UPB prime THEN prime[ SHORTEN n ]
ELIF NOT ODD n      THEN FALSE
ELSE
LONG INT f          :=  3;
LONG INT f2         :=  9;
LONG INT to next    := 16;
BOOL     is a prime := TRUE;
WHILE f2 <= n AND is a prime DO
is a prime := n MOD f /= 0;
f         +:= 2;
f2        +:= to next;
to next   +:= 8
OD;
is a prime
FI # is prime # ;
# sum the primes and test the sums                                        #
print( ( "The first 30 extreme primes:", newline ) );
print( ( whole( 2, -6 ), " " ) );  # 2 is the first prime so is "extreme" #
INT      prime sum count := 1;
LONG INT prime sum       := 2;
LONG INT candidate       := 1;
WHILE prime sum count < 5 000 DO
IF is prime( candidate +:= 2 ) THEN
prime sum +:= candidate;                    # have another prime #
IF is prime( prime sum ) THEN      # the prime sum is also prime #
prime sum count +:= 1;
IF prime sum count <= 30 THEN
print( ( whole( prime sum, -6 )
, IF prime sum count MOD 10 = 0 THEN newline ELSE " " FI
)
)
ELIF prime sum count MOD 1000 = 0 THEN
print( ( "Extreme prime ", whole( prime sum count, -5 )
, " is ",           whole( candidate,      -12 )
, ", sum: ",        whole( prime sum,      -18 )
, newline
)
)
FI
FI
FI
OD
END```
Output:
```The first 30 extreme primes:
2      5     17     41    197    281   7699   8893  22039  24133
25237  28697  32353  37561  38921  43201  44683  55837  61027  66463
70241  86453 102001 109147 116533 119069 121631 129419 132059 263171
Extreme prime  1000 is       196831, sum:         1657620079
Extreme prime  2000 is       495571, sum:         9744982591
Extreme prime  3000 is       808837, sum:        24984473177
Extreme prime  4000 is      1152763, sum:        49394034691
Extreme prime  5000 is      1500973, sum:        82195983953
```

C

Translation of: Wren
Library: GMP
```#include <stdio.h>
#include <locale.h>
#include <gmp.h>

int main() {
int i, m, extremes[30], count = 1;
mpz_t sum, p;
unsigned long usum, up;
extremes[0] = 2;
mpz_init_set_ui(sum, 2);
mpz_init_set_ui(p, 3);
setlocale(LC_NUMERIC, "");
while (1) {
if (mpz_probab_prime_p(sum, 5) > 0) {
++count;
if (count <= 30) {
extremes[count-1] = (int)mpz_get_ui(sum);
}
if (count == 30) {
printf("The first 30 extreme primes are:\n");
for (i = 0; i < 30; ++i) {
printf("%'7d ", extremes[i]);
if (!((i+1)%6)) printf("\n");
}
printf("\n");
} else if (!(count % 1000)) {
m = count / 1000;
if (m < 6 || m == 30 || m == 40 || m == 50) {
usum = mpz_get_ui(sum);
up = mpz_get_ui(p);
printf("The %'6dth extreme prime is: %'18ld for p <= %'10ld\n", count, usum, up);
if (m == 50) break;
}
}
}
mpz_nextprime(p, p);
}
mpz_clear(sum);
mpz_clear(p);
return 0;
}
```
Output:
```Identical to Wren output.
```

EasyLang

```fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
prim = 2
proc nextprim . .
repeat
prim += 1
until isprim prim = 1
.
.
while cnt < 30
n += prim
if isprim n = 1
cnt += 1
write n & " "
.
nextprim
.```
Output:
```2 5 17 41 197 281 7699 8893 22039 24133 25237 28697 32353 37561 38921 43201 44683 55837 61027 66463 70241 86453 102001 109147 116533 119069 121631 129419 132059 263171
```

FreeBASIC

```#include "isprime.bas"
Dim As Integer limit = 2000, n, c = 0
Dim As Integer Primes()

For n = 1 To limit
If isPrime(n) Then
c += 1
Redim Preserve Primes(n)
Primes(c) = n
End If
Next n

Print "The first 30 extreme primes are:"
Dim As Integer sum = 0, row = 0

For n = 1 To Ubound(Primes)
sum += Primes(n)
If isPrime(sum) Then
row += 1
Print Using "########"; sum;
If row Mod 10 = 0 Then Print
End If
Next n

Sleep```
Output:
`Similar to Ring entry.`

Go

Translation of: Wren
Library: Go-rcu

Based on Wren's GMP version but about 4 times slower as our GMP wrapper doesn't expose the Mpz_nextprime function. We're therefore using our own very simple version instead which is much slower.

```package main

import (
"fmt"
big "github.com/ncw/gmp"
"rcu"
)

func nextPrime(n *big.Int) *big.Int {
m := new(big.Int).Set(n)
z := new(big.Int)
zero := new(big.Int)
one := big.NewInt(1)
two := big.NewInt(2)
if z.Rem(m, two).Cmp(zero) == 0 {
} else {
}
for {
if m.ProbablyPrime(0) {
return m
}
}
}

func main() {
extremes := []int{2}
sum := big.NewInt(2)
count := 1
p := big.NewInt(3)
for {
if sum.ProbablyPrime(0) {
count++
if count <= 30 {
extremes = append(extremes, int(sum.Uint64()))
}
if count == 30 {
fmt.Println("The first 30 extreme primes are:")
rcu.PrintTable(extremes, 6, 7, true)
fmt.Println()
} else if count%1000 == 0 {
m := count / 1000
if m < 6 || m == 30 || m == 40 || m == 50 {
scount := rcu.Commatize(count)
ssum := rcu.Commatize(sum.Uint64())
sp := rcu.Commatize(p.Uint64())
fmt.Printf("The %6sth extreme prime is: %18s for p <= %10s\n", scount, ssum, sp)
if m == 50 {
return
}
}
}
}
p.Set(nextPrime(p))
}
}
```
Output:
```Identical to Wren output.
```

J

```   3 10\$(#~ 1&p:)+/\p:i.4e4
2     5     17     41    197    281   7699   8893  22039  24133
25237 28697  32353  37561  38921  43201  44683  55837  61027  66463
70241 86453 102001 109147 116533 119069 121631 129419 132059 263171
```

This would be more efficient if we had used 3e3 (216 extreme primes) rather than 4e4 (1942 extreme primes)

jq

Works with both jq and gojq, the C and Go implementations of jq ...

Using the generic utilities given immediately below, one solution to the problem of generating the first 30 extreme primes could be written as follows:

```def primes:
2 | recurse(nextprime);

def extremes:
foreach primes as \$p (0; . + \$p)
| select(is_prime);

limit(30; extremes)```

A program that solves both the primary and stretch tasks is given below.

Generic Utilities

```def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;

def nwise(\$n):
def n: if length <= \$n then . else .[0:\$n] , (.[\$n:] | n) end;
n;

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
(\$n | sqrt) as \$rt
| 23
| until( . > \$rt or (\$n % . == 0); .+2)
| . > \$rt
end;

def nextprime:
(if .%2==0 then 1 else 2 end) as \$n
| first(range(.+\$n; infinite;2) | select(is_prime));```

```{ extremes:[2],
sum:2,
p:3,
count:1 }
| while (.count <= 5000;
.emit = null
| .sum += .p
| if .sum|is_prime
then .count += 1
| if .count <= 30
then .extremes += [.sum]
| if .count == 30
then .emit = "The first 30 extreme primes are:\n"
| .emit += ([.extremes | nwise(10) | map(lpad(7)) | join(" ") ] | join("\n"))
| .emit += "\n"
else .
end
elif .count % 1000 == 0
then .emit = "The \(.count)th extreme prime is: \(.sum) for p <= \(.p)"
else .
end
else .
end
| .p |= nextprime
)
| .emit // empty```
Output:
```The first 30 extreme primes are:
2       5      17      41     197     281    7699    8893   22039   24133
25237   28697   32353   37561   38921   43201   44683   55837   61027   66463
70241   86453  102001  109147  116533  119069  121631  129419  132059  263171

The 1000th extreme prime is: 1657620079 for p <= 196831
The 2000th extreme prime is: 9744982591 for p <= 495571
The 3000th extreme prime is: 24984473177 for p <= 808837
The 4000th extreme prime is: 49394034691 for p <= 1152763
The 5000th extreme prime is: 82195983953 for p <= 1500973
```

Julia

```julia> using Primes

julia> n = 0
0

julia> for p in primes(2000) n += p; isprime(n) && println(n); end
2
5
17
41
197
281
7699
8893
22039
24133
25237
28697
32353
37561
38921
43201
44683
55837
61027
66463
70241
86453
102001
109147
116533
119069
121631
129419
132059
263171
```

Translation of: Python
```using Primes

let

ecount, p, n = 0, 0, 0

while ecount < 50_000
p = nextprime(p + 1)
n += p
if isprime(n)
ecount += 1
if ecount < 31
println("Sum of prime series up to \$p: prime \$n")
elseif ecount in [1000, 2000, 3000, 4000, 5000, 30_000, 40_000, 50_000]
println("Sum of \$ecount in prime series up to \$p: prime \$n")
end
end
end

end
```
Output:
```Sum of prime series up to 2: prime 2
Sum of prime series up to 3: prime 5
Sum of prime series up to 7: prime 17
Sum of prime series up to 13: prime 41
Sum of prime series up to 37: prime 197
Sum of prime series up to 43: prime 281
Sum of prime series up to 281: prime 7699
Sum of prime series up to 311: prime 8893
Sum of prime series up to 503: prime 22039
Sum of prime series up to 541: prime 24133
Sum of prime series up to 557: prime 25237
Sum of prime series up to 593: prime 28697
Sum of prime series up to 619: prime 32353
Sum of prime series up to 673: prime 37561
Sum of prime series up to 683: prime 38921
Sum of prime series up to 733: prime 43201
Sum of prime series up to 743: prime 44683
Sum of prime series up to 839: prime 55837
Sum of prime series up to 881: prime 61027
Sum of prime series up to 929: prime 66463
Sum of prime series up to 953: prime 70241
Sum of prime series up to 1061: prime 86453
Sum of prime series up to 1163: prime 102001
Sum of prime series up to 1213: prime 109147
Sum of prime series up to 1249: prime 116533
Sum of prime series up to 1277: prime 119069
Sum of prime series up to 1283: prime 121631
Sum of prime series up to 1307: prime 129419
Sum of prime series up to 1321: prime 132059
Sum of prime series up to 1949: prime 263171
Sum of 1000 in prime series up to 196831: prime 1657620079
Sum of 2000 in prime series up to 495571: prime 9744982591
Sum of 3000 in prime series up to 808837: prime 24984473177
Sum of 4000 in prime series up to 1152763: prime 49394034691
Sum of 5000 in prime series up to 1500973: prime 82195983953
Sum of 30000 in prime series up to 12437401: prime 4889328757567
Sum of 40000 in prime series up to 17245391: prime 9207632380589
Sum of 50000 in prime series up to 22272277: prime 15118097491121
```

Nim

 This example is incorrect. Please fix the code and remove this message.Details: outputting the next prime which was not added to ep (yet)
Library: Nim-Integers

We use third party package “integers” to get Miller-Rabin primality test.

```import std/[strformat, strutils]
import integers

echo "First 30 extreme primes:"
var ep = newInteger(0)
var count =  0
var lim = 1000
var p = newInteger(2)
while true:
ep += p
p = p.nextPrime
if ep.isPrime:
inc count
if count <= 30:
stdout.write &"{ep:>6}"
stdout.write if count mod 6 == 0: '\n' else: ' '
if count == 30: echo()
elif count == lim:
echo &"Sum of {count} in prime series up to {insertSep(\$p):>9}: prime {insertSep(\$ep):>14}"
inc lim, 1000
if lim > 5000: break
```
Output:
```First 30 extreme primes:
2      5     17     41    197    281
7699   8893  22039  24133  25237  28697
32353  37561  38921  43201  44683  55837
61027  66463  70241  86453 102001 109147
116533 119069 121631 129419 132059 263171

Sum of 1000 in prime series up to   196_837: prime  1_657_620_079
Sum of 2000 in prime series up to   495_587: prime  9_744_982_591
Sum of 3000 in prime series up to   808_853: prime 24_984_473_177
Sum of 4000 in prime series up to 1_152_773: prime 49_394_034_691
Sum of 5000 in prime series up to 1_500_991: prime 82_195_983_953
```

Phix

```with javascript_semantics
constant lim = 30
sequence extremes = {}
integer ep = 0, np = 0
while length(extremes)<lim do
np += 1; ep += get_prime(np)
if is_prime(ep) then extremes &= ep end if
end while
printf(1,"The first %d extreme primes are:\n%s\n",{lim,join_by(extremes,1,6,fmt:="%,7d")})
include mpfr.e
mpz z = mpz_init(ep)
integer found = 30, p
for tgt in {1e3,2e3,3e3,4e3,5e3,3e4,4e4,5e4} do
while found<tgt do
np += 2; p = get_prime(np)
if mpz_prime(z) then found += 1 end if
end while
string zs = mpz_get_str(z,10,true)
printf(1,"The %,dth extreme prime is %s (primes[1..%,d]<=%,d)\n",{tgt,zs,np,p})
end for
```
Output:
```The first 30 extreme primes are:
2         5        17        41       197       281
7,699     8,893    22,039    24,133    25,237    28,697
32,353    37,561    38,921    43,201    44,683    55,837
61,027    66,463    70,241    86,453   102,001   109,147
116,533   119,069   121,631   129,419   132,059   263,171

The 1,000th extreme prime is 1,657,620,079 (primes[1..17,722]<=196,831)
The 2,000th extreme prime is 9,744,982,591 (primes[1..41,198]<=495,571)
The 3,000th extreme prime is 24,984,473,177 (primes[1..64,596]<=808,837)
The 4,000th extreme prime is 49,394,034,691 (primes[1..89,504]<=1,152,763)
The 5,000th extreme prime is 82,195,983,953 (primes[1..114,236]<=1,500,973)
The 30,000th extreme prime is 4,889,328,757,567 (primes[1..814,900]<=12,437,401)
The 40,000th extreme prime is 9,207,632,380,589 (primes[1..1,106,004]<=17,245,391)
The 50,000th extreme prime is 15,118,097,491,121 (primes[1..1,405,244]<=22,272,277)
```

Python

```""" rosettacode.org/wiki/Extreme_primes """

from sympy import isprime, nextprime

ecount, p, n = 0, 0, 0

while ecount < 50_000:
p = nextprime(p)
n += p
if isprime(n):
ecount += 1
if ecount < 31:
print(f'Sum of prime series up to {p}: prime {n}')
if ecount in [1000, 2000, 3000, 4000, 5000, 30_000, 40_000, 50_000]:
print(
f'Sum of {ecount :,} in prime series up to {p :,}: prime {n :,}')
```
Output:
```Sum of prime series up to 2: prime 2
Sum of prime series up to 3: prime 5
Sum of prime series up to 7: prime 17
Sum of prime series up to 13: prime 41
Sum of prime series up to 37: prime 197
Sum of prime series up to 43: prime 281
Sum of prime series up to 281: prime 7699
Sum of prime series up to 311: prime 8893
Sum of prime series up to 503: prime 22039
Sum of prime series up to 541: prime 24133
Sum of prime series up to 557: prime 25237
Sum of prime series up to 593: prime 28697
Sum of prime series up to 619: prime 32353
Sum of prime series up to 673: prime 37561
Sum of prime series up to 683: prime 38921
Sum of prime series up to 733: prime 43201
Sum of prime series up to 743: prime 44683
Sum of prime series up to 839: prime 55837
Sum of prime series up to 881: prime 61027
Sum of prime series up to 929: prime 66463
Sum of prime series up to 953: prime 70241
Sum of prime series up to 1061: prime 86453
Sum of prime series up to 1163: prime 102001
Sum of prime series up to 1213: prime 109147
Sum of prime series up to 1249: prime 116533
Sum of prime series up to 1277: prime 119069
Sum of prime series up to 1283: prime 121631
Sum of prime series up to 1307: prime 129419
Sum of prime series up to 1321: prime 132059
Sum of prime series up to 1949: prime 263171
Sum of 1,000 in prime series up to 196,831: prime 1,657,620,079
Sum of 2,000 in prime series up to 495,571: prime 9,744,982,591
Sum of 3,000 in prime series up to 808,837: prime 24,984,473,177
Sum of 4,000 in prime series up to 1,152,763: prime 49,394,034,691
Sum of 5,000 in prime series up to 1,500,973: prime 82,195,983,953
Sum of 30,000 in prime series up to 12,437,401: prime 4,889,328,757,567
Sum of 40,000 in prime series up to 17,245,391: prime 9,207,632,380,589
Sum of 50,000 in prime series up to 22,272,277: prime 15,118,097,491,121
```

Raku

So we're just gonna keep doing the same task over and over with slightly different names?

Primes equal to the sum of the first k primes for some k.

```use Lingua::EN::Numbers;

say \$_».&comma».fmt("%7s").batch(10).join: "\n" for
(([\+] (^∞).grep: &is-prime).grep: &is-prime)[^30,999,1999,2999,3999,4999];
```
Output:
```      2       5      17      41     197     281   7,699   8,893  22,039  24,133
25,237  28,697  32,353  37,561  38,921  43,201  44,683  55,837  61,027  66,463
70,241  86,453 102,001 109,147 116,533 119,069 121,631 129,419 132,059 263,171
1,657,620,079
9,744,982,591
24,984,473,177
49,394,034,691
82,195,983,953```

Ring

```see "working..." + nl
limit = 2000
Primes = []

for n = 1 to limit
if isPrime(n)
ok
next
sum = 0
row = 0

for n = 1 to len(Primes)
sum = sum + Primes[n]
if isPrime(sum)
row++
see "" + sum + " "
if row % 10 = 0
see nl
ok
ok
next
see "done..." + nl

func isPrime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1```
Output:
```working...
2 5 17 41 197 281 7699 8893 22039 24133
25237 28697 32353 37561 38921 43201 44683 55837 61027 66463
70241 86453 102001 109147 116533 119069 121631 129419 132059 263171
done...
```

RPL

Works with: HP version 49
```« 0 → max sum
« { } 1
DO
NEXTPRIME
DUP 'sum' STO+
IF sum ISPRIME? THEN SWAP sum + SWAP END
UNTIL OVER SIZE max ≥ END
DROP2
» » ‘XPRIM’ STO
30 XPRIM
```
Output:
```1: { 2 5 17 41 197 281 7699 8893 22039 24133 25237 28697 32353 37561 38921 43201 44683 55837 61027 66463 70241 86453 102001 109147 116533 119069 121631 129419 132059 263171 }
```

Ruby

```require 'prime'

sum, n = 0, 30
extreme_primes = Prime.lazy.filter_map{|pr|sum += pr; [pr, sum] if sum.prime?}

puts "The first #{n} extreme primes are:"
extreme_primes.first(30).map(&:last).each_slice(10){|slice| puts "%8d"*slice.size % slice}

sum = 0
puts
extreme_primes.first(5000).each_slice(1000).with_index(1) do|slice, i|
puts "The %dth extreme prime is sum of primes upto %10d: %12d" % [i*1000, *slice.last]
end
```
Output:
```The first 30 extreme primes are:
2       5      17      41     197     281    7699    8893   22039   24133
25237   28697   32353   37561   38921   43201   44683   55837   61027   66463
70241   86453  102001  109147  116533  119069  121631  129419  132059  263171

The 1000th extreme prime is sum of primes upto     196831:   1657620079
The 2000th extreme prime is sum of primes upto     495571:   9744982591
The 3000th extreme prime is sum of primes upto     808837:  24984473177
The 4000th extreme prime is sum of primes upto    1152763:  49394034691
The 5000th extreme prime is sum of primes upto    1500973:  82195983953
```

Sidef

Translation of: Julia
```var(c,p,n) = (0,0,0)

while (c < 50_000) {
p.next_prime!
n += p
if (n.is_prime) {
++c
if (c <= 30) {
say "Sum of prime series up to #{p}: prime #{n}"
}
elsif (c ~~ [1000, 2000, 3000, 4000, 5000, 30_000, 40_000, 50_000]) {
say ("Sum of #{c.commify} in prime series up to #{p}: prime #{n}")
}
}
}
```
Output:
```Sum of prime series up to 2: prime 2
Sum of prime series up to 3: prime 5
Sum of prime series up to 7: prime 17
Sum of prime series up to 13: prime 41
Sum of prime series up to 37: prime 197
Sum of prime series up to 43: prime 281
Sum of prime series up to 281: prime 7699
Sum of prime series up to 311: prime 8893
Sum of prime series up to 503: prime 22039
Sum of prime series up to 541: prime 24133
Sum of prime series up to 557: prime 25237
Sum of prime series up to 593: prime 28697
Sum of prime series up to 619: prime 32353
Sum of prime series up to 673: prime 37561
Sum of prime series up to 683: prime 38921
Sum of prime series up to 733: prime 43201
Sum of prime series up to 743: prime 44683
Sum of prime series up to 839: prime 55837
Sum of prime series up to 881: prime 61027
Sum of prime series up to 929: prime 66463
Sum of prime series up to 953: prime 70241
Sum of prime series up to 1061: prime 86453
Sum of prime series up to 1163: prime 102001
Sum of prime series up to 1213: prime 109147
Sum of prime series up to 1249: prime 116533
Sum of prime series up to 1277: prime 119069
Sum of prime series up to 1283: prime 121631
Sum of prime series up to 1307: prime 129419
Sum of prime series up to 1321: prime 132059
Sum of prime series up to 1949: prime 263171
Sum of 1,000 in prime series up to 196831: prime 1657620079
Sum of 2,000 in prime series up to 495571: prime 9744982591
Sum of 3,000 in prime series up to 808837: prime 24984473177
Sum of 4,000 in prime series up to 1152763: prime 49394034691
Sum of 5,000 in prime series up to 1500973: prime 82195983953
Sum of 30,000 in prime series up to 12437401: prime 4889328757567
Sum of 40,000 in prime series up to 17245391: prime 9207632380589
Sum of 50,000 in prime series up to 22272277: prime 15118097491121```

Wren

Wren-CLI

Library: Wren-math
Library: Wren-fmt
```import "./math" for Int
import "./fmt" for Fmt

var extremes = [2]
var sum = 2
var p = 3
var count = 1
while (true) {
sum = sum + p
if (Int.isPrime(sum)) {
count = count + 1
if (count <= 30) {
}
if (count == 30) {
System.print("The first 30 extreme primes are:")
Fmt.tprint("\$,7d ", extremes, 6)
System.print()
} else if (count % 1000 == 0) {
Fmt.print("The \$,r extreme prime is: \$,14d for p <= \$,9d", count, sum, p)
if (count == 5000) return
}
}
p = Int.nextPrime(p)
}
```
Output:
```The first 30 extreme primes are:
2        5       17       41      197      281
7,699    8,893   22,039   24,133   25,237   28,697
32,353   37,561   38,921   43,201   44,683   55,837
61,027   66,463   70,241   86,453  102,001  109,147
116,533  119,069  121,631  129,419  132,059  263,171

The 1,000th extreme prime is:  1,657,620,079 for p <=   196,831
The 2,000th extreme prime is:  9,744,982,591 for p <=   495,571
The 3,000th extreme prime is: 24,984,473,177 for p <=   808,837
The 4,000th extreme prime is: 49,394,034,691 for p <= 1,152,763
The 5,000th extreme prime is: 82,195,983,953 for p <= 1,500,973
```

Embedded (GMP)

Library: Wren-gmp
```import "./gmp" for Mpz
import "./fmt" for Fmt

var extremes = [2]
var sum = Mpz.two
var count = 1
var p = Mpz.three
while (true) {
if (sum.probPrime(5) > 0) {
count = count + 1
if (count <= 30) {
}
if (count == 30) {
System.print("The first 30 extreme primes are:")
Fmt.tprint("\$,7i ", extremes, 6)
System.print()
} else if (count % 1000 == 0) {
var m = count / 1000
if (m < 6 || m == 30 || m == 40 || m == 50) {
Fmt.print("The \$,8r extreme prime is: \$,18i for p <= \$,10i", count, sum, p)
if (m == 50) return
}
}
}
p.nextPrime
}
```
Output:
```The first 30 extreme primes are:
2        5       17       41      197      281
7,699    8,893   22,039   24,133   25,237   28,697
32,353   37,561   38,921   43,201   44,683   55,837
61,027   66,463   70,241   86,453  102,001  109,147
116,533  119,069  121,631  129,419  132,059  263,171

The  1,000th extreme prime is:      1,657,620,079 for p <=    196,831
The  2,000th extreme prime is:      9,744,982,591 for p <=    495,571
The  3,000th extreme prime is:     24,984,473,177 for p <=    808,837
The  4,000th extreme prime is:     49,394,034,691 for p <=  1,152,763
The  5,000th extreme prime is:     82,195,983,953 for p <=  1,500,973
The 30,000th extreme prime is:  4,889,328,757,567 for p <= 12,437,401
The 40,000th extreme prime is:  9,207,632,380,589 for p <= 17,245,391
The 50,000th extreme prime is: 15,118,097,491,121 for p <= 22,272,277
```

XPL0

```include xpllib; \for IsPrime and RlOutC
int C, N, S;
[Text(0, "The first 30 extreme primes are:^m^j");
Format(7,0);
C:= 0;  N:= 2;  S:= 0;
loop    [if IsPrime(N) then
[S:= S+N;
if IsPrime(S) then
[C:= C+1;
RlOutC(0, float(S));
if rem(C/6) = 0 then CrLf(0);
if C >= 30 then quit;
];
];
N:= N+1;
];
]```
Output:
```The first 30 extreme primes are:
2        5       17       41      197      281
7,699    8,893   22,039   24,133   25,237   28,697
32,353   37,561   38,921   43,201   44,683   55,837
61,027   66,463   70,241   86,453  102,001  109,147
116,533  119,069  121,631  129,419  132,059  263,171
```