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


#include "isprime.bas"
 
Dim As Integer i = 0
Dim As Integer IndN = 1, IndM = 1
Dim As Integer NumP = 2, NumC = 4
Dim As Integer SumP = 2, SumC = 4
Print "               sum    prime sum     composite sum"
Do
    If SumC > SumP Then
        Do
            NumP += 1 
        Loop Until isPrime(NumP)
        SumP += NumP
        IndN += 1
    End If
    If SumP > SumC Then
        Do 
            NumC += 1 
        Loop Until Not isPrime(NumC)
        SumC += NumC
        IndM += 1
    End If
    If SumP = SumC Then
        Print Using "##,###,###,###,### - ##,###,###  - ##,###,###"; SumP; IndN; IndM
        i += 1
        If i >= 9 Then Exit Do
        Do
            NumC += 1
        Loop Until Not isPrime(NumC)
        SumC += NumC
        IndM += 1
    End If
Loop