Math Help - Prime- numbers

1. Prime- numbers

Find 15 prime numbers $p_{1},p_{2}.....,p_{15}$
and $p_{i}> 7$ :
$
p_{1}^{4}+p_{2}^{4}+p_{3}^{4}+p_{4}^{4}+...+p_{15} ^{4}=1499
$

2. Originally Posted by dhiab
Find 15 prime numbers $p_{1},p_{2}.....,p_{15}$
and $p_{i}> 7$ :
$
p_{1}^{4}+p_{2}^{4}+p_{3}^{4}+p_{4}^{4}+...+p_{15} ^{4}=1499
$
This doesn't even make sense.

$\sum_{j=1}^{15}p_j^4>15\cdot 7^4>1499$