login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002386 Increasing gaps between primes (lower end): primes p(k) where p(k+1)-p(k) exceeds p(j+1)-p(j) for all j<k.
(Formerly M0858 N0327)
90
2, 3, 7, 23, 89, 113, 523, 887, 1129, 1327, 9551, 15683, 19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201, 2010733, 4652353, 17051707, 20831323, 47326693, 122164747, 189695659, 191912783, 387096133, 436273009, 1294268491 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See the links by Jens Kruse Andersen et al. for very large gaps.

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 133.

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, Sect 6.1, Table 1.

M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 14.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

M. F. Hasler and N. J. A. Sloane, Table of n, a(n) for n=1..75

Jens Kruse Andersen, The Top-20 Prime Gaps

Jens Kruse Andersen, New largest known prime gap

Jens Kruse Andersen, Maximal gaps

Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.

Alexei Kourbatov, Upper Bounds for Prime Gaps Related to Firoozbakht’s Conjecture, arXiv preprint, 2015.

T. R. Nicely, List of prime gaps

T. R. Nicely, New maximal prime gaps and first occurrences, Math. Comput. 68,227 (1999) 1311-1315.

Tomás Oliveira e Silva, Gaps between consecutive primes

D. Shanks, On maximal gaps between successive primes, Math. Comp., 18 (1964), 646-651.

Eric Weisstein's World of Mathematics, Prime Gaps

J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224.

Index entries for primes, gaps between

FORMULA

a(n) = A000101(n) - A005250(n) = A008950(n-1) - 1. - M. F. Hasler, Dec 13 2007

A000720(a(n)) = A005669(n).

a(n) = A000040(A005669(n)). - M. F. Hasler, Apr 26 2014

MATHEMATICA

s = {2}; gm = 1; Do[p = Prime[n]; g = Prime[n + 1] - p; If[g > gm, Print[p]; AppendTo[s, p]; gm = g], {n, 2, 1000000}]; s   (* Jean-François Alcover, Mar 31 2011 *)

PROG

(PARI) a(n)=local(p, g); if(n<2, 2*(n>0), p=a(n-1); g=nextprime(p+1)-p; while(p=nextprime(p+1), if(nextprime(p+1)-p>g, break)); p) /* Michael Somos, Feb 07 2004 */

(PARI) p=q=2; g=0; until( g<(q=nextprime(1+p=q))-p & print1(q-g=q-p, ", "), ) \\ M. F. Hasler, Dec 13 2007

CROSSREFS

Cf. A001223, A000101 (upper ends), A005250 (record gaps), A000230.

Cf. A005669, A134266, A070866.

See also A205827(n) = A000040(A214935(n)), A182514(n) = A000040(A241540(n)).

Sequence in context: A088173 A129739 A163834 * A000230 A256454 A133429

Adjacent sequences:  A002383 A002384 A002385 * A002387 A002388 A002389

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Apr 30 1991

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified September 3 02:59 EDT 2015. Contains 261302 sequences.