Prime Numbers Composed of Strings of Consecutive Ascending Digits

Sequence
The sequence of prime numbers consisting of strings of consecutive ascending digits (allowing $0$ to follow $9$) begins:
 * $2, 3, 5, 7, 23, 67, 89, 4567, 78 \, 901, 678 \, 901, 23 \, 456 \, 789, 45 \, 678 \, 901, $
 * $9 \, 012 \, 345 \, 678 \, 901, 789 \, 012 \, 345 \, 678 \, 901, $
 * $56 \, 789 \, 012 \, 345 \, 678 \, 901 \, 234 \, 567 \, 890 \, 123, $
 * $90 \, 123 \, 456 \, 789 \, 012 \, 345 \, 678 \, 901 \, 234 \, 567, $
 * $678 \, 901 \, 234 \, 567 \, 890 \, 123 \, 456 \, 789 \, 012 \, 345 \, 678 \, 901$

It is not known whether there exist any more.