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The smaller member of a twin prime pair in which both primes are emirps.
2

%I #19 Apr 03 2023 10:36:12

%S 71,1031,1151,1229,3299,3371,3389,3467,3851,7457,7949,9011,9437,10007,

%T 10067,10457,10889,11159,11699,11717,11777,11969,12071,12107,13709,

%U 13757,14447,14549,14591,15731,16451,17207,17681,17747,17909,18911,19421,19541

%N The smaller member of a twin prime pair in which both primes are emirps.

%C Subsequence of A001359 and of A006567.

%H Metin Sariyar, <a href="/A175215/b175215.txt">Table of n, a(n) for n = 1..16451</a>

%H Green, Prime Curios, <a href="https://t5k.org/curios/page.php?curio_id=20903">Entry 71</a>

%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_973.htm">Puzzle 973. Largest known twin & emirp</a>, The Prime Puzzles & Problems Connection.

%p read("transforms") ; isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:

%p isA006567 := proc(n) local r ; r := digrev(n) ; isprime(n) and isprime(r) and n<> r ; end proc:

%p isA175215 := proc(n) isA001359(n) and isA006567(n) and isA006567(n+2) ; end proc:

%p for i from 1 to 10000 do p := ithprime(i) ; if isA175215(p) then printf("%d,",p) ; end if; end do: # _R. J. Mathar_, Mar 16 2010

%t Do[IR=IntegerReverse;Q=PrimeQ;If[Q[n]&&Q[n+2]&&Q[IR[n]]&&PrimeQ[IR[n+2]]&&!n==IR[n]&&!(n+2)==IR[n+2],Print[n]],{n,5,10^5,6}] (* _Metin Sariyar_, Dec 17 2019 *)

%o (Magma) emirp:=func<n|IsPrime(n) and IsPrime(Seqint(Reverse(Intseq(n)))) and Intseq(n) ne Reverse(Intseq(n))>; [p:p in PrimesUpTo(20000)| emirp(p) and emirp(p+2)]; // _Marius A. Burtea_, Dec 17 2019

%Y Cf. A001359, A006567.

%K nonn,base

%O 1,1

%A _Lekraj Beedassy_, Mar 06 2010

%E 11699 inserted, 14921 -> 19421 corrected by _R. J. Mathar_, Mar 16 2010