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# examples of Smarandache-Wellin primes in a few selected bases

In base 10, there are eight known Smarandache-Wellin primes. The first three are 2, 23 and 2357; these are listed in A069151 of Sloane’s OEIS. The fourth is approximately $2.357111317192329313741434753\times 10^{{355}}$, and the other four are much larger.

The first three binary Smarandache-Wellin primes are 2, 11 and 751, while in hexadecimal the first two are 2 and 144763. There are slightly more in octal: 2, 19, 157 and 440152287140627310757403395684438501207352921. By now it should be quite obvious that 2 is a Smarandache-Wellin prime regardless of the base.

The first few Smarandache-Wellin primes in factorial base are 2, …

This concept cannot be extended to Roman numerals, as the concatenations yield invalid combinations like IIIIIV and IIIIIVVII.

## Mathematics Subject Classification

11A63*no label found*

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