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%I #3 Sep 24 2013 09:24:38
%S 72353,1745153,7444673,44726593,49202147,61503553,100006817,100072097,
%T 101686177,107444417,143046977,214756067,257412163,430372577,
%U 431661313,435812033,447149537,452523713,489805633,530372321,744340577,834187553
%N Prime numbers that are the sum of three distinct positive eighth powers.
%C These are also the sum of three squares and the sum of three fourth powers: 7444673 = 16^2 + 1296^2 + 2401^2 = 4^4 + 36^4 + 49^4 = 256 + 1679616 + 5764801.
%e 72353 = 2^8 + 3^8 + 4^8 = 256 + 6561 + 65536.
%e 7444673 = 2^8 + 6^8 + 7^8 = 256 + 1679616 + 5764801.
%e 49202147 = 5^8 + 7^8 + 9^8 = 390625 + 5764801 + 43046721.
%o (PARI) {m=14;p=m^8;v=vector(m,x,x^8);w=[];for(i=1,m-2,for(j=i+1,m-1, for(k=j+1,m,if((n=v[i]+v[j]+v[k])<p&&isprime(n),w=concat(w,n))))); w=listsort(List(w),1);for(j=1,#w-1,print1(w[j],","))} /* Klaus Brockhaus, Feb 11 2007 */
%Y Cf. A125516, A126657.
%K nonn
%O 1,1
%A _Tomas Xordan_, Feb 09 2007
%E Edited, corrected and extended by _Klaus Brockhaus_, Feb 11 2007
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