Are there more non-trivial powers of the form $S_p$?

70 Views Asked by At

Let $S_p:=2+3+5+\cdots p$ denote the sum of primes up to $p$. I searched for $S_p$ being a non-trivial power and only found the following squares so far :

? s=0;forprime(p=1,10^9,s=s+p;if(ispower(s)>0,print(p,"  ",s,"   ",factor(s))))
23  100   [2, 2; 5, 2]
22073  25633969   [61, 2; 83, 2]
67187  212372329   [13, 2; 19, 2; 59, 2]
79427  292341604   [2, 2; 83, 2; 103, 2]
10729219  3672424151449   [463, 2; 4139, 2]
?

Are there more non-trivial powers $S_p$ ? In particular, are there any non-trivial powers $S_p$ besides squares ?