

A000101


Record gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps).
(Formerly M2485 N0984)


78



3, 5, 11, 29, 97, 127, 541, 907, 1151, 1361, 9587, 15727, 19661, 31469, 156007, 360749, 370373, 492227, 1349651, 1357333, 2010881, 4652507, 17051887, 20831533, 47326913, 122164969, 189695893, 191913031, 387096383, 436273291, 1294268779
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OFFSET

1,1


COMMENTS

See A002386 for complete list of known terms and further references.
Except for a(1)=3 and a(2)=5, a(n) = A168421(k). Primes 3 and 5 are special in that they are the only primes which do not have a Ramanujan prime between them and their double, <= 6 and 10 respectively. Because of the large size of a gap, there are many repeats of the prime number in A168421.  John W. Nicholson, Dec 10 2013


REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part IV, SpringerVerlag, see p. 133.
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

Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, and Terence Tao, Long gaps between primes, arXiv:1412.5029 [math.NT], 20142016.


FORMULA



MATHEMATICA

s = {3}; gm = 1; Do[p = Prime[n + 1]; g = p  Prime[n]; If[g > gm, Print[p]; AppendTo[s, p]; gm = g], {n, 2, 1000000}]; s (* JeanFrançois Alcover, Mar 31 2011 *)


PROG

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


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



STATUS

approved



