A136207 Primes p such that p-6 or p+6 is prime.

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 283, 307, 311, 313, 317, 331, 337

Offset: 1

Author

Carlos Alves, Dec 21 2007

Keywords

• nonn

Comments

Either or both of (p-6) and (p+6) is/are prime. - Harvey P. Dale, Jun 22 2019

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Math, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- _N. J. A. Sloane_, Mar 07 2021]
• Wikipedia, Sexy Primes

Crossrefs

Cf. A023201, A046117, A140546 (complement).

Programs

Maple

isA136207 := proc(n)
    if isprime(n) then
        if isprime(n+6) or isprime(n-6) then
            true;
        else
            false;
        end if;
    else
        false ;
    end if;
end proc:
A136207 := proc(n)
    option remember;
    local a;
    if n = 1 then
        5 ;
    else
        a := nextprime(procname(n-1)) ;
        while true do
            if isA136207(a) then
                return a;
            else
                a := nextprime(a) ;
            end if;
        end do:
    end if;
end proc:
seq(A136207(n),n=1..80) ; # R. J. Mathar, Jun 10 2024

Mathematica

dd = 6; DistancePrimesQ1 = (PrimeQ[ # ] && PrimeQ[ # + dd]) &; DistancePrimesQ2 = (PrimeQ[ # ] && PrimeQ[ # - dd] && (# > dd)) &; DistancePrimesQQ = (DistancePrimesQ1[ # ] || DistancePrimesQ2[ # ]) &; DistancePrimes = Select[Range[ # ], DistancePrimesQQ] &; DistancePrimes[1000]
Alternative by Lei Zhou:
p = 3; Table[While[p = NextPrime[p]; ! (PrimeQ[p - 6] || PrimeQ[p + 6])]; p, {n, 1, 100}]
Select[Prime[Range[3,100]],AnyTrue[#+{6,-6},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 22 2019 *)