A089202 Primes p such that p-2 and p+2 are divisible by a cube.

4457, 10987, 15377, 20873, 32587, 39877, 51109, 53377, 54623, 60127, 66877, 74873, 101873, 107377, 112997, 115589, 120877, 121123, 125197, 126443, 128873, 135623, 143719, 148957, 155377, 161053, 161377, 162623, 168127, 169373, 174877, 176123

Offset

1,1

Comments

For any distinct odd primes p,q, includes all primes == 2 (mod p^3) and == -2 (mod q^3), and thus is infinite by Dirichlet's theorem on primes in arithmetic progressions. Robert Israel, Jan 11 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

4457-2 = 3^4*5*11,4457+2 = 7^3*13

Maple

filter:= proc(p)
isprime(p) and ormap(t -> t[2]>=3, ifactors(p+2)[2]) and ormap(t -> t[2]>=3, ifactors(p-2)[2])
end proc:
select(filter, [seq(i, i=3..2*10^5, 2)]); # Robert Israel, Jan 11 2019

Mathematica

filterQ[p_] := PrimeQ[p] && AnyTrue[FactorInteger[p-2], #[[2]] >= 3&] && AnyTrue[FactorInteger[p+2], #[[2]] >= 3&];
Select[Prime[Range[20000]], filterQ] (* Jean-François Alcover, Aug 26 2020 *)

Prog

(PARI) powerfreep4(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(!ispowerfree(x-k, p) && !ispowerfree(x+k, p), c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) } ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) }

Crossrefs

Sequence in context: A253704 A235015 A185767 * A250977 A289513 A345590

Adjacent sequences: A089199 A089200 A089201 * A089203 A089204 A089205

Keyword

easy,nonn

Author

Cino Hilliard, Dec 08 2003

Status

approved