A353249 Primes that are the sum of the cubes of four primes, not necessarily distinct.

89, 149, 367, 383, 503, 601, 1709, 2221, 2357, 4001, 4937, 5171, 6599, 6883, 7019, 7237, 7243, 7583, 9091, 10177, 11261, 11807, 14747, 15923, 16693, 17431, 24413, 24767, 25673, 26539, 27059, 30169, 32587, 34739, 43517, 48731, 51031, 51347, 53201, 53323, 53699, 54133, 59617

Offset: 1

Author

Michel Marcus, Apr 08 2022

Keywords

• nonn

Examples

			89 is a term because 2^3 + 3^3 + 3^3 + 3^3 = 89.
15923 is a term because 2^3 + 13^3 + 19^3 + 19^3 = 15923.
		

Links

• Zhichun Zhai, Problems related to Waring-Goldbach problem involving cubes of primes, arXiv:2201.07346 [math.GM], 2022. See Table 1 p. 3 but some terms are missing.

Crossrefs

Primes in A346917.

Cf. A123597.

Programs

Maple

q:= proc(n, t) option remember; `if`(n=0, is(t=0), t>0 and
      ormap(p-> isprime(p) and q(n-p^3, t-1), [$2..iroot(n, 3)]))
    end:
select(x-> isprime(x) and q(x, 4), [$1..60000])[];  # Alois P. Heinz, Apr 08 2022

Mathematica

seq[max_] := Module[{s = Select[Range[Floor@Surd[max, 3]], PrimeQ]}, Select[Union[Plus @@@ (Tuples[s, 4]^3)], # <= max && PrimeQ[#] &]]; seq[60000] (* Amiram Eldar, Apr 08 2022 *)

PARI

isok(p) = {if (isprime(p) && (p > 24), my(P=primes(primepi(sqrtn(p-24, 3)+1))); for (i=1, #P, for (j=i, #P, for (k=j, #P, for (n=k, #P, if (P[i]^3 + P[j]^3 + P[k]^3 + P[n]^3 == p, return (1)););););););}