login
Primes that contain only the digits (5, 7, 8).
2

%I #16 Sep 08 2022 08:46:13

%S 5,7,557,577,587,757,787,857,877,887,5557,5857,7577,7757,7877,8887,

%T 55787,57557,57587,57787,58757,58787,75557,75577,75787,77557,77587,

%U 78577,78787,78857,78877,78887,85577,87557,87587,87877,87887,555557,555857,557857,558587

%N Primes that contain only the digits (5, 7, 8).

%C A020467 and A020470 are subsequences.

%H Alois P. Heinz, <a href="/A260830/b260830.txt">Table of n, a(n) for n = 1..10000</a>

%H James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019)

%t Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 7, 8}] == {} &]

%t Select[Flatten[Table[FromDigits/@Tuples[{5,7,8},n],{n,6}]],PrimeQ] (* _Harvey P. Dale_, Oct 06 2017 *)

%o (Magma) [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [5,7,8]];

%Y Cf. similar sequences listed in A260827.

%Y Cf. A020467, A020470.

%K nonn,easy,base

%O 1,1

%A _Vincenzo Librandi_, Aug 02 2015