A173874 Primes in A173836.

29, 41, 101, 173, 191, 197, 383, 1019, 1049, 1091, 1163, 1409, 1481, 1613, 1637, 1721, 1823, 1913, 1973, 2027, 2099, 2243, 2339, 2351, 2447, 2729, 2837, 2897, 2999, 3023, 3089, 3137, 3167, 3203, 3251, 3407, 3881, 4019, 4349, 4397, 4451, 4457

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 01 2010

Keywords

• base
• nonn

Comments

For a prime p and its k-digit cube p^3 we need to check if q = 11^3 * 10^k + p^3 is a prime.

11^3*10^k is congruent to 2 (mod 3), so p^3 must be congruent to 2 (mod 3) because otherwise the sum q cannot become a prime.

In turn, all p in the sequence are also congruent to 2 (mod 3) (see A003627).

Examples

			The prime 29 is in the sequence because 29^3=24389, and the concatenation 133124389=prime(7545294) is a prime number.
		

References

• K. Haase and P. Mauksch: Spass mit Mathe, Urania-Verlag Leipzig, Verlag Dausien Hanau, 2. Auflage 1985

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000578, A168147, A168219, A173579, A173733, A173836

Programs

Maple

cat2 := proc(a,b) ndgs := max(1, ilog10(b)+1) ; a*10^ndgs+b ; end proc:
for i from 1 to 800 do p := ithprime(i) ; if isprime(cat2(1331,p^3)) then printf("%d,",p) ; end if; end do: # R. J. Mathar, Mar 26 2010

Mathematica

Select[Prime[Range[2000]],PrimeQ[FromDigits[Join[{1,3,3,1}, IntegerDigits[ #^3]]]]&] (* Harvey P. Dale, Oct 14 2011 *)

Extensions

Definition simplified, missing numbers 2243, 2339 etc. inserted, numbers like 2621, 2693 removed - R. J. Mathar, Mar 26 2010