Inmathematics, aSmarandache–Wellin number is aninteger that in a givenbase is theconcatenation of the firstnprime numbers written in that base. Smarandache–Wellin numbers are named afterFlorentin Smarandache andPaul R. Wellin.

The firstdecimal Smarandache–Wellin numbers are:

2,23,235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, ... (sequenceA019518 in theOEIS).

A Smarandache–Wellin number that is also prime is called aSmarandache–Wellin prime. The first three are 2, 23 and 2357 (sequenceA069151 in theOEIS). 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, ... (sequenceA046284 in theOEIS).

The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:

1, 2, 4, 128, 174, 342, 435, 1429, ... (sequenceA046035 in theOEIS).

The 1429th Smarandache–Wellin number is a prime with 5719 digits ending in 11927, discovered byEric W. Weisstein as aprobable 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]

• Copeland–Erdős constant
• Champernowne constant, another example of a number obtained by concatenating a representation in a given base.

• Weisstein, 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 atThe Prime Glossary
• Smith, S. "A Set of Conjectures on Smarandache Sequences." Bull. Pure Appl. Sci. 15E, 101–107, 1996.

• Base-dependent integer sequences
• Prime numbers

• Articles with short description
• Short description is different from Wikidata
• Wikipedia pages semi-protected from banned users