OFFSET
1,1
COMMENTS
(1) These primes all with end digit 1=1^3 are concatenations of two CUBIC numbers: "n^3 1".
(2) It is conjectured that the sequence is infinite.
(3) It is an open problem if 3 consecutive naturals n exist which give such a prime.
No three such integers exist, as every n = 2 (mod 3) yields 10n^3 + 1 = 0 (mod 3). - Charles R Greathouse IV, Apr 24 2010
REFERENCES
Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = 10*A168219(n)^3 + 1. \\ M. F. Hasler, Jul 24 2011
MATHEMATICA
Select[Table[10*n^3+1, {n, 1000}], PrimeQ] (* Vincenzo Librandi, Aug 01 2012 *)
PROG
(PARI) for(n=1, 2e2, isprime(n^3*10+1) && print1(n^3*10+1", ")) \\ M. F. Hasler, Jul 24 2011
(Magma) [ a: n in [1..150] | IsPrime(a) where a is 10*n^3+1 ]; // Vincenzo Librandi, Jul 25 2011
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 19 2009
STATUS
approved