OFFSET
1,1
COMMENTS
No more terms with m < 5000. - Vincenzo Librandi, Jan 03 2014
From Jeppe Stig Nielsen, Feb 05 2022 (Start)
Exponent m must be zero or a power of two. Because if m>0 has a nontrivial odd divisor, then the polynomial X^m+Y^m is reducible, and the corresponding number 10^m+7^m has an algebraic factor.
It can be conjectured that no more terms exist. From the factordb.com link it can be inferred that for any new terms the exponent m must be at least 2^23.
Factors of larger candidates are being collected, see Keller link.
(End)
LINKS
Wilfrid Keller, Factors of generalized Fermat numbers found after Björn & Riesel
Markus Tervooren, factordb.com, Factors of 10^(2^n)+7^(2^n)
MATHEMATICA
Select[Table[7^m + 10^m, {m, 0, 1500}], PrimeQ] (* Vincenzo Librandi, Jan 03 2014 *)
PROG
(Magma) [a: m in [0..1500] | IsPrime(a) where a is 7^m+10^m];
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Apr 29 2010
STATUS
approved