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

43, 59, 67, 83, 89, 97, 107, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383

Offset: 1

Author

Reinhard Zumkeller, Nov 19 2002

Keywords

• nonn

Comments

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

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

Examples

			A000040(25) = 97 = 3^3 + 3^3 + 3^3 + 2^3 + 2^3, therefore 97 is a term.
		

Links

• Eric Weisstein's World of Mathematics, Cubic Number.
• Index entries for sequences related to sums of cubes
• Hiroshi Mikawa and Temenoujka Peneva, Sums of Five Cubes of Primes in Short Intervals.

Crossrefs

Cf. A000578, A078128, A078133, A000040, A078138.

Primes in A122612.