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%I #25 Jun 14 2021 14:50:02
%S 46,51,55,71,99,119,164,298,345,461,509,523,588,668,779,827,844,848,
%T 999,1100,1151,1215,1306,1321,1408,1553,1568,1616,1779,1900,1931,1953,
%U 2102,2150,2221,2444,2653,2677,3116,3405,3527,3731,3776,3890,3898,3989,4070,4188,4257,4546,4556,4574,4681,4694,4846,4947,4948,4974
%N Integers n such that the concatenation of prime(n) and prime(n+1) and also concatenation of prime(n+1) and prime(n) are prime.
%C Difference between prime(n) and prime(n+1) is a multiple of 6, otherwise concatenation prime(n)//prime(n+1) is divisible by 3.
%H Zak Seidov, <a href="/A269671/b269671.txt">Table of n, a(n) for n = 1..59542</a>
%e prime(46)=199, prime(47)=211 and both 199211 and 211199 are prime,
%e prime(51)=233, prime(51)=239 and both 233239 and 239233 are prime,
%e prime(9999972)=179424263, prime(9999973)=179424269 and both 179424263179424269 and 179424269179424263 are prime.
%t PrimePi/@Select[Partition[Prime[Range[5000]],2,1],AllTrue[{FromDigits[ Join[ IntegerDigits[ #[[1]]],IntegerDigits[#[[2]]]]],FromDigits[ Join[ IntegerDigits[#[[2]]],IntegerDigits[#[[1]]]]]},PrimeQ]&][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 14 2021 *)
%o (PARI) isok(n) = {my(sp = Str(prime(n))); my(sq = Str(prime(n+1))); isprime(eval(concat(sp, sq))) && isprime(eval(concat(sq, sp)));} \\ _Michel Marcus_, Mar 07 2016
%Y Cf. A088712, A088784.
%K nonn,base
%O 1,1
%A _Zak Seidov_, Mar 07 2016
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