OFFSET
0,1
COMMENTS
a(11) <= 79419801290172271035479303914142441 and a(12) <= 55128448018333565337014555712123010955456071077000028555991469751. - Abhiram R Devesh, Aug 09 2014
From Zhining Yang, Dec 02 2022: (Start)
a(11) = 5333419265419188034369535864125349, 34 digits, discovered by Helmut Spielauer in 2013
a(12) = 55128448018333565337014555712123010955456071077000028555991469751, 65 digits, discovered by Helmut Spielauer in 2013
a(13) = 192180552346991956641101827551986346298837407139466361414211497406670710665021150917759713696699494356609164354068319457039591759, 129 digits, discovered by Dana Jacobsen in 2016
a(14) = 267552521*631#/210 - 9606, 268 digits, discovered by Dana Jacobsen in 2016
a(15) = 2717*1303#/268590 - 16670, 552 digits, discovered by Dana Jacobsen in 2014
a(16) = 7079*3559#/9870 - 36310, 1517 digits, discovered by Michiel Jansen, Pierre Cami, and Jens Kruse Andersen in 2013
a(17) = 1111111111111111111*9059#/(11#*5237) - 86522, 3899 digits, discovered by Hans Rosenthal in 2017
a(11) to a(17) were searched from Thomas R. Nicely's homepage. (End)
LINKS
C. Hilliard, TwinPrimes Java code.
Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101].
Thomas R. Nicely, Other tables of prime gaps
FORMULA
a(n) = A000230(2^(n-1)). - R. J. Mathar, Jan 12 2007
a(n) = A000230(2^(n-1)) = Min{p|nextprime(p)-p = 2^n} [may need adjusting since offset has been changed].
EXAMPLE
a(2)=7 because 7 and 11 are consecutive primes with difference 2^2=4.
a(3)=89 because 89 and 97 are consecutive primes with difference 2^3=8.
MATHEMATICA
f[n_] := Block[{k = 1}, While[Prime[k + 1] != n + Prime[k], k++ ]; Prime[k]]; Do[ Print[ f[2^n]], {n, 0, 10}] (* Robert G. Wilson v, Jan 13 2005 *)
PROG
(Python)
import sympy
n=0
while n>=0:
....p=2
....while sympy.nextprime(p)-p!=(2**n):
........p=sympy.nextprime(p)
....print(p)
....n=n+1
....p=sympy.nextprime(p)
## Abhiram R Devesh, Aug 09 2014
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 25 2001
EXTENSIONS
a(10) sent by Robert G. Wilson v, Jan 13 2005
STATUS
approved