OFFSET
1,1
EXAMPLE
p1=prime[(n + 1)^2], p= prime[n^2], p1-p2=q^3: n = 79, p1 = 63809, p = 62081, q = 12; n = 10288, p1 = 2163941687, p = 2163502711, q = 76; n = 16181, p1 = 5602364903, p = 5601635903, q = 90; n = 306998, p1=2596139184841, p = 2596121608841, q = 260. n = 394021, p1 = 4357072887373, p = 4357049981069, q = 284. Next n, if any, is > 500000.
MATHEMATICA
Select[Range[400000], IntegerQ[(Prime[(#+1)^2]-Prime[#^2])^(1/3)]&] (* Harvey P. Dale, Dec 13 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 07 2008
STATUS
approved