Perhaps the n-th term begins with the concatenation of the first n-1 primes, except for n = 3.
The 9th, 11th, 12th, 13th, .... terms are other counterexamples to the above "conjecture". On the other hand, it seems almost sure that the n-th term starts with the concatenation of the first n-2 primes. - M. F. Hasler, Mar 20 2011
There are counterexamples to Hasler as well. For example, a(23) = 235711131719232931374147535961677173798997 (which misses 43). Such extreme cases are more likely to happen near boundaries when the number of digits in the primes increases. - Sean A. Irvine, Jan 28 2026
