A030459 Prime p concatenated with next prime is also prime.

2, 31, 83, 151, 157, 167, 199, 233, 251, 257, 263, 271, 331, 353, 373, 433, 467, 509, 523, 541, 601, 653, 661, 677, 727, 941, 971, 1013, 1033, 1181, 1187, 1201, 1223, 1259, 1367, 1453, 1459, 1657, 1669, 1709, 1741, 1861, 1973, 2069, 2161

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Terms 157, 257, 263, 541, 1187, 1459, 2179 also belong to A030460. - Carmine Suriano, Jan 27 2011

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

Links

• M. F. Hasler and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 4110 terms from Hasler)

Crossrefs

See A030461 for the concatenated primes.

Cf. A000720, A030460, A045533, A151799.

Programs

Mathematica

Select[Prime[Range[500]],PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[ NextPrime[#]]]]]&] (* Harvey P. Dale, Jun 20 2011 *)

PARI

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

Formula

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

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