In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first nprime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
A Smarandache–Wellin number that is also prime is called a Smarandache–Wellin prime. The first three are 2, 23 and 2357 (sequence A069151 in the OEIS). The fourth is 355 digits long: it is the result of concatenating the first 128 prime numbers, through 719.[1]
The primes at the end of the concatenation in the Smarandache–Wellin primes are
2, 3, 7, 719, 1033, 2297, 3037, 11927, ... (sequence A046284 in the OEIS).
The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:
1, 2, 4, 128, 174, 342, 435, 1429, ... (sequence A046035 in the OEIS).
The 1429th Smarandache–Wellin number is a probable prime with 5719 digits ending in 11927, discovered by Eric W. Weisstein in 1998.[2] If it is proven prime, it will be the eighth Smarandache–Wellin prime. In March 2009, Weisstein's search showed the index of the next Smarandache–Wellin prime (if one exists) is at least 22077.[3]
List of first 54 Smarandache–Wellin numbers with factorizations
Smarandache–Wellin primes at The Prime Glossary
Smith, S. "A Set of Conjectures on Smarandache Sequences." Bull. Pure Appl. Sci. 15E, 101–107, 1996.
January 01, 1970
smarandache, wellin, number, mathematics, integer, that, given, base, concatenation, first, prime, numbers, written, that, base, named, after, florentin, smarandache, paul, wellin, first, decimal, 2357, 235711, 23571113, 2357111317, 235711131719, 2357111317192. In mathematics a Smarandache Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base Smarandache Wellin numbers are named after Florentin Smarandache and Paul R Wellin The first decimal Smarandache Wellin numbers are 2 23 235 2357 235711 23571113 2357111317 235711131719 23571113171923 2357111317192329 sequence A019518 in the OEIS Contents 1 Smarandache Wellin prime 2 See also 3 References 4 External linksSmarandache Wellin primeA Smarandache Wellin number that is also prime is called a Smarandache Wellin prime The first three are 2 23 and 2357 sequence A069151 in the OEIS The fourth is 355 digits long it is the result of concatenating the first 128 prime numbers through 719 1 The primes at the end of the concatenation in the Smarandache Wellin primes are 2 3 7 719 1033 2297 3037 11927 sequence A046284 in the OEIS The indices of the Smarandache Wellin primes in the sequence of Smarandache Wellin numbers are 1 2 4 128 174 342 435 1429 sequence A046035 in the OEIS The 1429th Smarandache Wellin number is a probable prime with 5719 digits ending in 11927 discovered by Eric W Weisstein in 1998 2 If it is proven prime it will be the eighth Smarandache Wellin prime In March 2009 Weisstein s search showed the index of the next Smarandache Wellin prime if one exists is at least 22077 3 See alsoCopeland Erdos constant Champernowne constant another example of a number obtained by concatenating a representation in a given base References Pomerance Carl B Crandall Richard E 2001 Prime Numbers a computational perspective Springer pp 78 Ex 1 86 ISBN 0 387 25282 7 Rivera Carlos Primes by Listing Weisstein Eric W Integer Sequence Primes MathWorld Retrieved 2011 07 28 External linksWeisstein Eric W Smarandache Wellin number MathWorld Weisstein Eric W Smarandache Wellin prime MathWorld Smarandache Wellin number PlanetMath List of first 54 Smarandache Wellin numbers with factorizations Smarandache Wellin primes at The Prime Glossary Smith S A Set of Conjectures on Smarandache Sequences Bull Pure Appl Sci 15E 101 107 1996 Retrieved from https en wikipedia org w index php title Smarandache Wellin number amp oldid 1128400757, wikipedia, wiki, book, books, library,
