A114787 Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

0, 53, 0, 557, 55511, 55555555555555555555555555555555555555555555555555555555555555555555513, 55555517, 5519, 523, 55529, 5531, 0, 541, 55555543, 547, 55555553, 55555559

Offset

1,2

Comments

Prime(n) is all zeros followed by prime(n). This is all fives followed by prime(n).

The next sequence in this progression, "Smallest prime of the form: all sixes followed by prime(n), a(n)> prime(n)", begins 0, 0, 0, 67, then (5) = 2*(10^5039 - 1)/3 - 55, a number that consists of 5037 sixes followed by 2 ones. This does not fit into the constraints of the OEIS. N. J. A. Sloane, Nov 20 2005, based on information from Hans Havermann.

The large number is quickly certified prime by PARI's APRCL test: isprime(555...513,2) -> 1. - Hagen von Eitzen, Jun 17 2009

Next term is 5*(10^184 - 1)/9 + 6, containing 184 digits, and is too large to include here. - Arkadiusz Wesolowski, Jun 03 2013

Links

Table of n, a(n) for n=1..17.

Example

a(5) = 55511, as 511, 5511 are composite, prime(5) = 11.
All positive numbers of the form 5*(10^k - 1)/9 - 18 have a factor in the covering set {3, 7, 13, 37}, so a(12) = 0. - Arkadiusz Wesolowski, Jun 03 2013

Crossrefs

Cf. A114783, A114784, A114785, A114786.

Sequence in context: A208300 A038778 A116107 * A198776 A367821 A051320

Adjacent sequences: A114784 A114785 A114786 * A114788 A114789 A114790

Keyword

base,nonn

Author

Amarnath Murthy, Nov 17 2005

Extensions

More terms from Joshua Zucker, May 06 2006

Edited by T. D. Noe, Oct 30 2008

a(12)-a(17) from Arkadiusz Wesolowski, Jun 03 2013

Status

approved