cp's OEIS Frontend

A078132 Primes which can be written as sum of cubes > 1.

%I A078132 #10 Feb 16 2025 08:32:48
%S A078132 43,59,67,83,89,97,107,113,131,137,139,149,151,157,163,167,173,179,
%T A078132 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,
%U A078132 277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383
%N A078132 Primes which can be written as sum of cubes > 1.
%C A078132 Equivalent to primes which can be written as the sum of cubes of primes; the question being "what is the minimum number of terms in such sums when they can be written in more than one way? - _Jonathan Vos Post_, Sep 21 2006
%C A078132 Mikawa and Peneva: "One of the famous and still unsettled problems in additive prime number theory is the conjecture that every sufficiently large integer satisfying some natural congruence conditions, can be written as the sum of four cubes of primes. Although the present methods lack the power to prove such a strong result, Hua... has been able to prove that every sufficiently large odd integer as the sum of nine cubes of primes. He also established that almost all integers {n == 1 mod 2, n =/= 0, +/-2 mod 9, n =/= 0 mod 7} can be expressed as the sum of five cubes of primes." - _Jonathan Vos Post_, Sep 21 2006
%H A078132 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>.
%H A078132 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%H A078132 Hiroshi Mikawa and Temenoujka Peneva, <a href="http://mathweb.sc.niigata-u.ac.jp/ant/Sympo/rims05_abst/mikawa_peneva.pdf">Sums of Five Cubes of Primes in Short Intervals</a>.
%e A078132 A000040(25) = 97 = 3^3 + 3^3 + 3^3 + 2^3 + 2^3, therefore 97 is a term.
%Y A078132 Cf. A000578, A078128, A078133, A000040, A078138.
%Y A078132 Primes in A122612.
%K A078132 nonn
%O A078132 1,1
%A A078132 _Reinhard Zumkeller_, Nov 19 2002