This puzzle is a variation
of another posted by Claudio Meller as the entry
1398 in his always interesting site.
Here we ask for these
numbers N that result prime numbers after inserting the
first consecutive primes, one at a a time, from 2 to P,
except the prime "3" in successive positions in N, from
left to right.
Example: N=333 is a
solution because 2333, 3533,
3373 and 33311
are prime numbers.
As a matter of fact,
below 2^32 I have found 21 of these asked numbers N,
being the smallest "27" and largest "2653294371".
Find more solutions.