OFFSET
1,1
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).
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
EXAMPLE
The prime 29 is in the sequence because 29^3=24389, and the concatenation 133124389=prime(7545294) is a prime number.
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 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 01 2010
EXTENSIONS
Definition simplified, missing numbers 2243, 2339 etc. inserted, numbers like 2621, 2693 removed - R. J. Mathar, Mar 26 2010
STATUS
approved