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, ... (sequence A019518 in OEIS).
Smarandache-Wellin primes
A Smarandache-Wellin number that is also prime is called a Smarandache-Wellin prime. The first three are 2, 23 and 2357 (A069151). The fourth has 355 digits and ends with the digits 719.[1]
The primes at the end of the concatenation in the Smarandache-Wellin primes are
- 2, 3, 7, 719, 1033, 2297, 3037, 11927?, ... (A046284).
The indices of the Smarandache-Wellin primes in the sequence of Smarandache-Wellin numbers are:
- 1, 2, 4, 128, 174, 342, 435, 1429?, ... (A046035).
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 July 2006 Weisstein's search showed the index of the next Smarandache-Wellin prime (if one exists) is greater than 18272.[3]
See also
References
- ^ Pomerance, Carl B.; Crandall, Richard E. (2001). Prime Numbers: a computational perspective. Springer, p78 Ex 1.86. ISBN 0387252827.
- ^ Rivera, Carlos, Primes by Listing
- ^ Eric W. Weisstein, Integer Sequence Primes at MathWorld.
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