A Smarandache number emerges by concatenating the first $n$ positive integers in increasing order in base $\ 10\ $.
The Smarandache numbers (See http://mathworld.wolfram.com/SmarandacheNumber.html) have been checked for primality upto a very high level. None is known.
If we concatencate in decreasing order , the numbers are , if I remember right , called reversed Smarandache numbers.
I also think I have found somewhere that they have also been checked but cannot find this link anymore.
With pfgw and the command Smr(n) , those numbers can easily be checked. So far, I only found $\ Smr(82)\ $ as a (proven) prime of the form Smr(n). Upto $\ n=6\ 000\ $ , no other prime Smr(n) exist.
Is another prime Smr(n) known , and if no, upto which limit have those numbers been checked ?
Best Answer
The OEIS sequence is http://oeis.org/A176024 which has only one further entry at $Smr(37765)$.
Following links leads to
http://mathworld.wolfram.com/ConsecutiveNumberSequences.html
and then to Mersenne Forum posts from
https://www.mersenneforum.org/showthread.php?p=415559
which indicate a search has been done and no further primes occur up to $Smr(99999)$.