A200474 a(n) = floor(10*(prime(n+1)-prime(n))/log(prime(n))^2).

3, 6, 2, 4, 6, 1, 5, 3, 1, 2, 4, 3, 1, 3, 2, 1, 3, 2, 3, 3, 1, 0, 1, 0, 1, 6, 1, 2, 0, 4, 0, 2, 2, 1, 2, 2, 0, 3, 0, 1, 0, 4, 4, 1, 0, 1, 2, 0, 3, 1, 1, 1, 0, 1, 1, 0, 3, 4, 1, 0, 1, 4, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 0, 1, 1, 1, 2, 1, 0, 1, 3

Offset: 5

Author

Arkadiusz Wesolowski, Nov 18 2011

Keywords

• nonn

Comments

Cramer's conjecture is true if, for every n >= 5, a(n) is smaller than 10.

If Cramer's conjecture is true, then Andrica's conjecture is true. [John W. Nicholson, Feb 06 2012]

Some mathematicians are trying to prove: if Andrica's conjecture is true, then Cramer's conjecture is true. [Arkadiusz Wesolowski, Feb 22 2012]

Examples

			a(9) = 6 because 10*(29-23)/log(23)^2 = 6.1029419977....
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 5..10000
• Carlos Rivera, Conjecture 7. The Cramer's Conjecture, The Prime Puzzles and Problems Connection.
• Eric Weisstein's World of Mathematics, Cramer Conjecture

Crossrefs

Cf. A000040, A001223, A086142, A124129, A200324.

Programs

Mathematica

Table[Floor[10*(Prime[n + 1] - Prime[n])/Log[Prime[n]]^2], {n, 5, 100}]

Formula

a(n) = floor(10*A001223(n)/log(A000040(n))^2), n >= 5.