A072236 Numbers of primes between successive primorials.

1, 2, 7, 36, 297, 2905, 39083, 603698, 11637502, 288086265, 7728273214, 251460107734, 9155428058351, 353182833587645, 15035130777416118, 726840450530910033, 39326730322451969003, 2211193504550790268932, 137315317472893091758587

Offset: 0

Author

Stephan Wagler (stephanwagler(AT)aol.com), Jul 05 2002

Keywords

• nonn
• hard
• more

Examples

			There are 3 primes less than 6, 7 primes between 6 and 30 and 36 primes between 30 and 210.
		

Links

• Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x) [From _Donovan Johnson_, Apr 25 2010]

Crossrefs

Cf. A002110, A000849.

Programs

Mathematica

Table[ PrimePi[ Product[Prime[i], {i, 1, n}]] - PrimePi[ Product[ Prime[i], {i, 1, n - 1}]], {n, 1, 12}]
Join[{1},Differences[PrimePi/@Rest[FoldList[Times,1,Prime[Range[12]]]]]] (* Harvey P. Dale, Mar 16 2012 *) (* Mathematica's implementation of PrimePi will not work for the 13th primorial because it's too large *)

Formula

a(n) = A000849(n+1) - A000849(n). - Amiram Eldar, Jun 11 2024

Extensions

Edited by Robert G. Wilson v, Jul 08 2002

a(13)-a(14) from Donovan Johnson, Apr 25 2010

a(15)-a(18) calculated using the data at A000849 and added by Amiram Eldar, Jun 11 2024