A008950 Increasing length runs of consecutive composite numbers (starting points).

4, 8, 24, 90, 114, 524, 888, 1130, 1328, 9552, 15684, 19610, 31398, 155922, 360654, 370262, 492114, 1349534, 1357202, 2010734, 4652354, 17051708, 20831324, 47326694, 122164748, 189695660, 191912784, 387096134, 436273010, 1294268492

Offset: 1

Author

Mark Cramer (m.cramer(AT)qut.edu.au). Computed by Dennis Yelle (dennis(AT)netcom.com)

Keywords

• nonn
• nice

Comments

There are runs of n consecutive composite numbers for every n. For example, the n numbers (n+1)!+2 ... (n+1)!+n+1 are composite. Such a run may start of course earlier than this. - Joerg Arndt, May 01 2013

Links

• Jens Kruse Andersen, Table of n, a(n) for n=1..74 (using A002386)
• Jens Kruse Andersen, The Top-20 Prime Gaps
• Jens Kruse Andersen, New record prime gap
• Jens Kruse Andersen, Maximal gaps
• Eric Weisstein's World of Mathematics, Prime Gaps.
• J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224.

Crossrefs

Cf. A008995, A008996.

Programs

Mathematica

maxGap = 1; Reap[Do[p = Prime[n]; gap = Prime[n+1] - p; If[gap > maxGap, Print[p+1]; Sow[p+1]; maxGap = gap], {n, 2, 10^8 }]][[2, 1]] (* Jean-François Alcover, Jun 15 2012 *)

Formula

a(n) = A002386(n+1)+1.

a(n) <= (n+1)! + 2. [Joerg Arndt, May 01 2013]