N SQRT SET_OF_PRIMES
3   7  { 13, 17, 19} 
3  11  { 37, 41, 43}
3  29  {277,281,283} 
3  31  {313,317,331}
5  31  {181,191,193,197,199} 
5  41  {317,331,337,347,349}
7  13  { 13, 17, 19, 23, 29, 31, 37}
7  47  {293,307,311,313,317,331,337}
9  29  { 73, 79, 83, 89, 97,101,103,107,109} 
9  47  {227,229,233,239,241,251,257,263,269}

From observation, where the square root of the sum of N consecutive primes to be prime N must be odd. Yet not all integer square roots for odd N are prime, as some are composites.

Composites for odd N of N consecutive primes < 500:
N SQRT SET_OF_PRIMES
5  33  {199,211,223,227,229}
7  25  { 73, 79, 83, 89, 97,101,103} 
9  10  {  2,  3,  5,  7, 11, 13, 17, 19, 23}

Composites for even N of N consecutive primes < 500:
N SQRT SET_OF_PRIMES
2   6  { 17, 19} 
2  10  { 47, 53}
2  12  { 71, 73} 
2  24  {283,293} 
4   6  {  5,  7, 11, 13}
4  18  { 73, 79, 83, 89} 
4  24  {137,139,149,151} 
4  42  {433,439,443,449} 
8  38  {163,167,173,179,181,191,193,197}

Posted by Dej Mar on 2011-03-07 04:55:49