OFFSET
1,1
COMMENTS
For n>0, let k be the multiplicity of 2 in the prime factorization of n (with k=0 if n is odd); then 31^(2^k)+10^(2^k) divides 31^n+10^n, so 31^(2^k)+10^(2^k) is a proper divisor of 31^n+10^n unless n=2^k. Thus the only values of n>0 at which 31^n+10^n can yield a prime are those where n=2^k. 31^(2^k)+10^(2^k) is composite for all 1<k<14, so the next term after 1061, if it exists, is at least 31^(2^14)+10^(2^14) (a 24435-digit number). - Jon E. Schoenfield, Jul 31 2010
PROG
(Magma) [ a: n in [0..1200] | IsPrime(a) where a is 31^n+10^n ];
CROSSREFS
KEYWORD
nonn,bref,more
AUTHOR
Vincenzo Librandi, Apr 29 2010
EXTENSIONS
Confirmed by N. J. A. Sloane, Jun 22 2010
STATUS
approved