A Smarandache prime is a prime Smarandache number, i.e., a prime number of the form 1234...n. 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 77000 to 200000 was completed by Balatov (2015b), and search of larger terms is now underway (Great Smarandache PRPrime search). As of Jun. 2018, it is known that there are no Smarandache primes up to index 10^6. This is consistent with the expected number of primes among the first million terms: about 0.6 (E. W. Mayer, Oct 09 2015, in OEIS A007908).

consecutive number sequences | integer sequence primes | Smarandache number | Smarandache sequences