OFFSET
1,1
COMMENTS
Conjecture: For any integer m > 0, there are infinitely many positive integers n such that all those gaps prime(n+i+1) - prime(n+i) (i = 0, ..., m-1) belong to the set {g > 0: g - 1 and g + 1 are twin prime}.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..50
EXAMPLE
a(1) = 754205 with those prime(754205+i+1) - prime(754205+i) (i = 0, ..., 12) having respective values 4, 12, 18, 42, 30, 30, 6, 12, 18, 30, 18, 12, 12 in the set {g > 0: g - 1 and g + 1 are twin prime}.
MATHEMATICA
d[n_]:=Prime[n+1]-Prime[n]
m=0; Do[Do[If[PrimeQ[d[n+i]-1]==False||PrimeQ[d[n+i]+1]==False, Goto[aa]], {i, 0, 12}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 9072188}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jun 25 2014
STATUS
approved