OFFSET
1,1
COMMENTS
No other n<10^12. There is a conjecture that this sequence is finite.
No other terms < 10^18. - Jud McCranie, Nov 03 2013
No other terms < 4.5*10^18. - Giovanni Resta, Apr 28 2014
EXAMPLE
The prime-free ranges are (2^3,3^2), (5^2,3^3), (2^5,6^2), (11^2,5^3), (3^7,13^3), (5^5,56^2), (181^2,2^15), (43^3,282^2), (46^3,312^2), (22434^2,55^5).
MATHEMATICA
lim=10^12; lst={}; k=2; While[n=Floor[lim^(1/k)]; n>=2, lst=Join[lst, Range[2, n]^k]; k++ ]; lst=Union[lst]; PrimeFree[n1_, n2_] := Module[{n=n1+1}, While[n<n2&&!PrimeQ[n], n++ ]; n ==n2]; lst2={}; Do[If[PrimeFree[lst[[i]], lst[[i+1]]], AppendTo[lst2, lst[[i]]]], {i, Length[lst]-1}]; lst2
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Mar 28 2006
STATUS
approved