cp's OEIS Frontend

A168375 Natural numbers n for which the concatenation p= "1 n^3" (A168327) is prime.

%I A168375 #4 Jul 22 2025 07:30:21
%S A168375 1,3,13,33,39,103,109,123,139,163,169,171,181,183,207,211,289,297,303,
%T A168375 309,339,369,379,393,423,451,457,463,1021,1027,1047,1053,1057,1081,
%U A168375 1087,1111,1123,1161,1189,1201,1249,1273,1293,1303,1329,1339,1351,1381,1387
%N A168375 Natural numbers n for which the concatenation p= "1 n^3" (A168327) is prime.
%C A168375 It is conjectured that sequence is infinite
%D A168375 Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
%D A168375 Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991
%D A168375 Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996
%F A168375 If n^3 is a d-digit natural number, odd and no multiple of 5, and d no multiple of 3, then p=10^d+n^3
%e A168375 (1) "1 1^3"=10^1+1^3=11=prime(5) gives a(1)=1
%e A168375 (2) "1 3^3"=10^2+3^3=127=prime(31) gives a(2)=3
%e A168375 (3) "1 13^3"=10^4+13^3=12197=prime(1458) gives a(3)=13
%Y A168375 Cf. A000040 The prime numbers
%Y A168375 Cf. A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
%Y A168375 Cf. A168327 Primes of concatenated form p= "1 n^3"
%Y A168375 Cf. A167535 Concatenation of two square numbers which give a prime
%K A168375 nonn,base
%O A168375 1,2
%A A168375 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 24 2009
%E A168375 Edited by _Charles R Greathouse IV_, Apr 23 2010