

A213677


Numbers n such that n and n + 12 are prime and there is a power of two in the interval (n, n+12).


1



5, 7, 11, 29, 31, 59, 61, 127, 251, 509, 1019, 1021, 262139, 1048571, 2147483647
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.


LINKS



PROG

(Magma)
//Program finds primes separated by an even number (called gap) which
//have a power of two between them. Program starts with the smallest
//power of two above gap. Primes less than this starting point can be
//checked by inspection.
gap:=12;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
powerof2:=2^i;
for k:=powerof2gap+1 to powerof21 by 2 do
if (IsPrime(k) and IsPrime(k+gap)) then k;
end if;
end for;
end for;


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



