Problems & Puzzles: Puzzles

Puzzle 1098 A Follow-up to puzzle 265

In our puzzle 265 we asked for the earliest integer having k distinct primes embedded, (as substrings).

For example: 137 is the earliest number that has embedded 5 distinct primes: 3, 7, 13, 37 & 137

Dmitry Kamenetsky proposes the following open questions:

The 10 digit number 1797193373 has 29 distinct substrings that are prime (see https://oeis.org/A093301).

Q1. Can you find a 20 digit number that has the most distinct prime substrings?

Q2. What about a 50 digit or a 100 digit number?


 

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