user
Suppose we have a sequence of prime sums, where each term **Pn** is the sum of the first **n** primes.

```
P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ...

```

```
P = 2, 5, 10, 17, 28, etc.

```

Further; suppose we have a sequence of composite sums, where each term **Cm** is the sum of the first **m** composites.

```
C = (4), (4 + 6), (4 + 6 + 8), (4 + 6 + 8 + 9), (4 + 6 + 8 + 9 + 10), ...

```

```
C = 4, 10, 18, 27, 37, etc.

```

Notice that the third term of **P**; **P3** (**10**) is equal to the second term of **C**; **C2** (**10**);

Task

* Find and display the indices (**n**, **m**) and value of at least the first 6 terms of the sequence of numbers that are both the sum of the first **n** primes and the first **m** composites.

See also

* OEIS:A007504 - Sum of the first n primes * OEIS:A053767 - Sum of first n composite numbers * OEIS:A294174 - Numbers that can be expressed both as the sum of first primes and as the sum of first composites
assistant
Let it run until I got bored and killed it. Time is total accumulated seconds since program start.

```
use Lingua::EN::Numbers:ver<2.8.2+>;

my $prime-sum =     [\+] (2..*).grep:  *.is-prime;
my $composite-sum = [\+] (2..*).grep: !*.is-prime;

my $c-index = 0;

for ^∞ -> $p-index {
    next if $prime-sum[$p-index] < $composite-sum[$c-index];
    printf( "%20s - %11s prime sum, %12s composite sum   %5.2f seconds\n",
      $prime-sum[$p-index].&comma, ordinal-digit($p-index + 1, :u, :c),
      ordinal-digit($c-index + 1, :u, :c), now - INIT now )
      and next if $prime-sum[$p-index] == $composite-sum[$c-index];
    ++$c-index;
    redo;
};

```

Output:

```
                  10 -         3ʳᵈ prime sum,          2ⁿᵈ composite sum    0.01 seconds
               1,988 -        33ʳᵈ prime sum,         51ˢᵗ composite sum    0.01 seconds
              14,697 -        80ᵗʰ prime sum,        147ᵗʰ composite sum    0.02 seconds
              83,292 -       175ᵗʰ prime sum,        361ˢᵗ composite sum    0.03 seconds
           1,503,397 -       660ᵗʰ prime sum,      1,582ⁿᵈ composite sum    0.04 seconds
          18,859,052 -     2,143ʳᵈ prime sum,      5,699ᵗʰ composite sum    0.08 seconds
          93,952,013 -     4,556ᵗʰ prime sum,     12,821ˢᵗ composite sum    0.14 seconds
      89,171,409,882 -   118,785ᵗʰ prime sum,    403,341ˢᵗ composite sum    4.23 seconds
   9,646,383,703,961 - 1,131,142ⁿᵈ prime sum,  4,229,425ᵗʰ composite sum   76.23 seconds
 209,456,854,921,713 - 5,012,372ⁿᵈ prime sum, 19,786,181ˢᵗ composite sum  968.26 seconds
^C
```