A090121 Numbers n such that nextprime(n^3)-prevprime(n^3) = 4.

2, 129, 189, 369, 435, 549, 555, 561, 819, 1245, 1491, 1719, 1779, 1839, 1875, 1935, 2175, 2289, 2415, 2451, 2595, 2709, 2769, 3141, 3441, 4401, 4611, 4851, 5655, 5775, 6075, 6099, 6795, 6969, 7125, 7239, 7365, 8109, 8139, 8325, 8361, 8385, 8535, 8685, 9591

Offset: 1

Author

Labos Elemer, Jan 12 2004

Keywords

• nonn

Examples

			n=129:{p=2146687,n^3=2146689,q=2146691}, q-p=4.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077038, A058043, A090122-A090125, A178228.

Programs

Mathematica

pre[x_] := Prime[PrimePi[x]] nex[x_] := Prime[PrimePi[x]+1] de[x_] := Prime[PrimePi[x]+1]-Prime[PrimePi[x]] k=3;Do[If[Equal[Prime[PrimePi[n^k]+1]-Prime[PrimePi[n^k]], 4], Print[n]], {n, 2, 100000}]
lst={};Do[m=n^3;If[PrimeQ[m-2]&&PrimeQ[m+2],AppendTo[lst,n]],{n,0,10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 04 2008 *)
Select[Range[2,6100],NextPrime[#^3]-NextPrime[#^3,-1]==4&] (* Harvey P. Dale, Sep 17 2017 *)

PARI

is(n)=if(n%2, isprime(n^3-2) && isprime(n^3+2), n==2) \\ Charles R Greathouse IV, Feb 22 2018

Formula

Solutions to A077038(x) = 4.

Extensions

More terms from Harvey P. Dale, Sep 17 2017