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, $

$678 \, 901 \, 234 \, 567 \, 890 \, 123 \, 456 \, 789 \, 012 \, 345 \, 678 \, 901$

This sequence is A006055 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

It is not known whether there exist any more.

Sources

• 1972: J.S. Madachy: Consecutive-digit primes - again (J. Recr. Math. Vol. 5, no. 4: pp. 253 – 254)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $23,456,789$