OFFSET
1,1
COMMENTS
Conjecture: For any integer m > 0, there are infinitely many positive integers n such that (prime(n+i+1) - prime(n+i))/2 is prime for every i = 0, ..., m-1.
Note that for n = 10377594 all those (prime(n+i+1) - prime(n+i))/2 (i = 0, ..., 15) are prime.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..93
EXAMPLE
a(1) = 56290 with (prime(56290+i+1) - prime(56290+i))/2 (i=0..12) having prime values 5, 3, 3, 7, 3, 5, 7, 11, 19, 2, 3, 3, 3 respectively.
MATHEMATICA
d[n_]:=(Prime[n+1]-Prime[n])/2
m=0; Do[Do[If[PrimeQ[d[n+i]]==False, Goto[aa]], {i, 0, 12}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 4901245}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jun 25 2014
STATUS
approved