A062530 Smallest prime p such that there is a gap of 2^n between p and previous prime.

3, 5, 11, 97, 1847, 5623, 89753, 3851587, 1872852203, 1999066711903, 22790428875365903, 5333419265419188034369535864127397, 55128448018333565337014555712123010955456071077000028555991473847

Offset: 0

Author

Labos Elemer, Jun 25 2001

Keywords

• nonn
• hard
• more

Comments

The next two terms are <= 13615411331526592827872074749865096844383295034548454421 and 768784577114627305753353689789300110953010089817032096740065409732504678169114467301254783622575120297131239844 respectively. - Larry Reeves (larryr(AT)acm.org), Jun 13 2002

Examples

			a(2) = 11 because 7 and 11 are consecutive primes with difference 4. - _Sascha Kurz_, Mar 05 2002
		

Links

• Thomas R. Nicely, First occurrence prime gaps. [For local copy see A000101]

Crossrefs

Cf. A000230, A062529, A151800.

Programs

PARI

a(n) = {q = 2; p = nextprime(q+1); gap = 2^n; while(p - q != gap, q = p; p = nextprime(p+1)); p;} \\ Michel Marcus, Dec 26 2013

Formula

a(n) = A000230(2^(n-1)) + 2^n = Min{p | p-prevprime(p) = 2^n}. - Amarnath Murthy, Feb 24 2002

a(n) = A151800(A062529(n)). - Amiram Eldar, Nov 04 2024

Extensions

More terms from Sascha Kurz, Mar 05 2002

Further terms from Larry Reeves (larryr(AT)acm.org), Jun 13 2002

Edited by N. J. A. Sloane Aug 31 2009 at the suggestion of R. J. Mathar

a(11)-a(12) calculated from the data at A062529 by Amiram Eldar, Nov 04 2024