A Smarandache prime is a prime Smarandache number, i.e., a prime number of the form . Surprisingly, no Smarandache primes are known as of Nov. 2015. Upper limits on the non-appearance of primes are summarized in the table below. The search from  to  was completed by Balatov (2015b), and search of larger terms is now underway (Great Smarandache PRPrime search). As of Dec. 2016, it is known that there are no Smarandache primes up to index 344869.

	reference
200	Fleuren (1999)
	E. Weisstein (Mar. 21, 2009)
	E. Weisstein (Oct. 17, 2011)
	M. Alekseyev (Oct. 3, 2015)
	S. Batalov (Oct. 22 2015)
	The Great Smarandache PRPrime search (Dec. 5, 2016)

If all digit substrings are allowed (so that e.g., concatenating just the 1 from 10, just 10111 from 101112, etc. are permitted), prime digit sequences are known. In particular, such primes are Champernowne-constant primes, the first few of which are 1234567891, 12345678910111, ... (OEIS A176942), which have 10, 14, 24, 235, 2804, 4347, 37735, ... decimal digits (OEIS A071620).

REFERENCES:

--. "The Great Smarandache PRPrime search." https://smarandache.ddns.net:1200/server_stats.html.

Balatov, S. "Smarandache Prime(s)." https://www.mersenneforum.org/showpost.php?p=412039&postcount=1. Oct. 5, 2015a.

Balatov, S. https://www.mersenneforum.org/showpost.php?p=413399&postcount=78. Oct 22, 2015b.

Fleuren, M. "Smarandache Factors and Reverse Factors." Smarandache Notions J. 10, 5-38, 1999.

Sloane, N. J. A. Sequences A071620 and A176942 in "The On-Line Encyclopedia of Integer Sequences."