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A030459 Prime p concatenated with next prime is also prime. 25

%I #24 Apr 11 2020 04:58:56

%S 2,31,83,151,157,167,199,233,251,257,263,271,331,353,373,433,467,509,

%T 523,541,601,653,661,677,727,941,971,1013,1033,1181,1187,1201,1223,

%U 1259,1367,1453,1459,1657,1669,1709,1741,1861,1973,2069,2161

%N Prime p concatenated with next prime is also prime.

%C Terms 157, 257, 263, 541, 1187, 1459, 2179 also belong to A030460. - _Carmine Suriano_, Jan 27 2011

%C All terms, except for the first one, must be either in A185934 or in A185935, i.e., have the same residue (mod 6) as the subsequent prime. - _M. F. Hasler_, Feb 06 2011

%H M. F. Hasler and Charles R Greathouse IV, <a href="/A030459/b030459.txt">Table of n, a(n) for n = 1..10000</a> (first 4110 terms from Hasler)

%F a(n) = A151799(A030460(n)).

%F A030461(n) = concat(a(n), A030460(n)) = A045533(A000720(a(n))).

%t Select[Prime[Range[500]],PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[ NextPrime[#]]]]]&] (* _Harvey P. Dale_, Jun 20 2011 *)

%o (PARI) o=2;forprime(p=3,1e4, isprime(eval(Str(o,o=p))) & print1(precprime(p-1)",")) \\ _M. F. Hasler_, Feb 06 2011

%Y See A030461 for the concatenated primes.

%Y Cf. A000720, A030460, A045533, A151799.

%K nonn,base

%O 1,1

%A _Patrick De Geest_

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Last modified April 25 01:35 EDT 2024. Contains 371964 sequences. (Running on oeis4.)