|
|
A136207
|
|
Primes p such that p-6 or p+6 is prime.
|
|
5
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Either or both of (p-6) and (p+6) is/are prime. - Harvey P. Dale, Jun 22 2019
|
|
LINKS
|
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]
|
|
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:
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:
|
|
MATHEMATICA
|
dd = 6; DistancePrimesQ1 = (PrimeQ[ # ] && PrimeQ[ # + dd]) &; DistancePrimesQ2 = (PrimeQ[ # ] && PrimeQ[ # - dd] && (# > dd)) &; DistancePrimesQQ = (DistancePrimesQ1[ # ] || DistancePrimesQ2[ # ]) &; DistancePrimes = Select[Range[ # ], DistancePrimesQQ] &; DistancePrimes[1000]
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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|