A153050 Six-digit squares that are concatenation of two 3-digit primes.

101761, 113569, 127449, 131769, 137641, 149769, 167281, 199809, 349281, 439569, 463761, 491401, 641601, 683929, 797449

Offset: 1

Author

Zak Seidov, Dec 17 2008

Keywords

• fini
• full
• nonn
• base

Comments

a(n)=(A153048(n))^2.

There are exactly 15 such numbers.

Crossrefs

Cf. A153048.

Programs

Mathematica

c = 0; t = 1000; re = Sort[Reap[Do[If[PrimeQ[p], Do[If[PrimeQ[q], r = p*t + q; s = Sqrt[r]; If[s == Floor[s], c++; Sow[r]]], {q, 101, 999, 2}]], {p, 101, 999, 2}]][[2, 1]]]
concatpQ[n_]:=Module[{idn=IntegerDigits[n],a,b},a=FromDigits[Take[idn,3]];b=FromDigits[Take[idn,-3]];IntegerLength[a]==IntegerLength[b]==3 && PrimeQ[a]&&PrimeQ[b]]; Select[Range[316,1000]^2,concatpQ] (* Harvey P. Dale, Mar 09 2012 *)