Smarandache–Wellin number
Template:Short description Template:Pp-sock 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).
Smarandache–Wellin prime
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
The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:
The 1429th Smarandache–Wellin number is a prime with 5719 digits ending in 11927, discovered by Eric W. Weisstein as a probable prime in 1998[2] and then proven prime in 2022.[3] In March 2009, Weisstein's search showed the index of the next Smarandache–Wellin prime (if one exists) is at least 22077.[4]
See also
- Copeland–Erdős constant
- Champernowne constant, another example of a number obtained by concatenating a representation in a given base.
References
External links
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- Template:Planetmath reference
- 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.
Template:Prime number classes Template:Classes of natural numbers
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- ↑ Rivera, Carlos, Primes by Listing
- ↑ Script error: No such module "citation/CS1".
- ↑ Script error: No such module "Template wrapper". Retrieved 2011-07-28.